Question 1

A trader marks the price of a television 30 percent above its cost price and then offers a discount of 10 percent on the marked price. As a result, he earns a profit of Rs. 340 on the sale. What is the cost price of the television set?

Accepted Answer

Introduction / Context: This question is a straightforward application of profit and loss along with markup and discount. The trader first increases the price by a certain percentage over cost, then offers a discount, and the net effect is a given profit in rupees. The goal is to recover the cost price from the given profit information. Given Data / Assumptions: Cost price of the television = C (unknown). Marked price (MP) = C increased by 30 percent. Discount offered on marked price = 10 percent. Net profit earned by the trader = Rs. 340. Concept / Approach: Markup and discount are applied successively. First the cost price is increased to get the marked price, and then discount is applied to get the selling price. The net profit is selling price minus cost price. By expressing the selling price as a percentage of cost price, we can directly relate profit to cost and solve for the unknown cost price using the given absolute profit in rupees. Step-by-Step Solution: Let cost price be C rupees. Marked price = C * (1 + 30 / 100) = 1.30 * C. Discount on marked price = 10 percent, so selling price SP = 1.30 * C * (1 - 10 / 100). Thus SP = 1.30 * C * 0.90 = 1.17 * C. Profit = SP - C = 1.17 * C - C = 0.17 * C. Given profit = Rs. 340, so 0.17 * C = 340. C = 340 / 0.17 = 2000 rupees. Verification / Alternative check: Cost price = Rs. 2000. Marked price = 2000 * 1.30 = Rs. 2600. Selling price after 10 percent discount = 2600 * 0.90 = Rs. 2340. Profit = 2340 - 2000 = Rs. 340, which matches the given profit. Therefore cost price is confirmed as Rs. 2000. Why Other Options Are Wrong: Rs. 1600, Rs. 2100, Rs. 2200: If you repeat the same markup and discount steps for these cost prices, the resulting profit will not be equal to Rs. 340. They correspond to incorrect manipulation of percentages or arithmetic mistakes. Common Pitfalls: Candidates sometimes subtract or add percentages directly without applying them in the correct sequence. Another mistake is to apply the discount on cost price instead of on marked price. Always remember that discount is calculated on marked price, and profit is ultimately based on cost price compared with final selling price. Final Answer: The cost price of the television is Rs. 2000.

Question 2

A shopkeeper sells an article at an 8 percent loss. If he increases the selling price of the article by Rs. 164, he earns a profit of 2.25 percent on the cost price. If he instead sells the article for Rs. 1760, what percentage profit does he make?

Accepted Answer

Introduction / Context: This question belongs to profit and loss with changes in selling price. The shopkeeper initially sells at a loss, but when he increases the selling price by a fixed amount, he gains a small profit. From these two conditions we can determine the cost price, and then compute the profit percent for another given selling price. This structure is common in competitive exams. Given Data / Assumptions: Initial selling price leads to an 8 percent loss. When the selling price is increased by Rs. 164, the profit becomes 2.25 percent. We need the profit percent if the article is sold for Rs. 1760. Cost price is constant in all the scenarios. Concept / Approach: The profit or loss percent is always based on cost price, whereas the difference between two selling prices is just a fixed rupee amount. The change from loss to profit gives the total change in profit, which equals the difference of the two selling prices. That relationship allows us to solve for the cost price. Once cost price is known, profit percent for any new selling price is straightforward to calculate. Step-by-Step Solution: Let the cost price be C rupees. Initial selling price SP1 corresponds to 8 percent loss, so SP1 = C * (1 - 8 / 100) = 0.92 * C. New selling price SP2 is SP1 + 164 and gives 2.25 percent profit. Thus SP2 = C * (1 + 2.25 / 100) = 1.0225 * C. Therefore 1.0225 * C - 0.92 * C = 164. So 0.1025 * C = 164. C = 164 / 0.1025 = 1600 rupees. Now consider the selling price of Rs. 1760. Profit at SP = 1760 = 1760 - 1600 = 160 rupees. Profit percent = 160 / 1600 * 100 = 10 percent. Verification / Alternative check: Check SP1: SP1 = 0.92 * 1600 = Rs. 1472. Loss at SP1 = 1600 - 1472 = Rs. 128, which is 8 percent of 1600. SP2 should be SP1 + 164 = 1472 + 164 = Rs. 1636. Profit at SP2 = 1636 - 1600 = Rs. 36, which is 36 / 1600 * 100 = 2.25 percent. All conditions are satisfied, therefore cost price and profit percentage for Rs. 1760 are correct. Why Other Options Are Wrong: 2.5%, 5%, and 7.5%: These profit percentages do not match the profit of Rs. 160 on cost price Rs. 1600. Only 10 percent matches the correct calculation using the derived cost price. Common Pitfalls: A frequent mistake is to assume that the difference between loss percent and profit percent directly translates into the rupee difference in selling prices without scaling by cost price. Another error is misinterpreting 2.25 percent as a fraction or using approximate values carelessly. Always write selling prices in terms of cost price and use their difference to solve for the unknown cost. Final Answer: When the article is sold for Rs. 1760, the shopkeeper makes a profit of 10%.

Question 3

Books are bought at prices between Rs. 200 and Rs. 350 each and are sold at prices between Rs. 300 and Rs. 425 each. What is the maximum possible total profit that can be made by selling eight books under these conditions?

Accepted Answer

Introduction / Context: This problem asks for the greatest possible profit when buying and selling items within given price ranges. It is a typical optimization question in profit and loss where you must choose the most favorable buying and selling prices within the allowed bounds. Given Data / Assumptions: Cost price of each book lies between Rs. 200 and Rs. 350. Selling price of each book lies between Rs. 300 and Rs. 425. Total number of books traded = 8. We are asked to find the maximum possible total profit. Concept / Approach: To maximize profit, the trader should buy each book at the lowest possible cost price and sell each book at the highest possible selling price within the given ranges. The profit per book is the difference between selling price and cost price. Then multiply maximum profit per book by the total number of books to get the maximum total profit. Step-by-Step Solution: Lowest possible cost price per book = Rs. 200. Highest possible selling price per book = Rs. 425. Maximum profit per book = 425 - 200 = Rs. 225. Number of books = 8. Maximum total profit = 225 * 8. 225 * 8 = 1800 rupees. Verification / Alternative check: If any book is bought at more than Rs. 200 or sold for less than Rs. 425, profit per book decreases. Hence choosing cost price strictly greater than 200 or selling price strictly less than 425 can never give a higher total profit than 225 rupees per book. Therefore the maximum profit configuration is indeed cost price at 200 and selling price at 425 for all eight books. Why Other Options Are Wrong: 800 and 1200 and 1600: These profits would arise if the price difference between buying and selling was smaller than the maximum 225 per book. Given the allowed ranges, the largest possible gap is 225 rupees, so any total profit smaller than 1800 rupees is suboptimal. Common Pitfalls: Some candidates incorrectly try to average the bounds instead of choosing extremes. Others think that cost and selling prices must be equal for all books or that there are constraints not mentioned in the problem. Unless stated otherwise, you are free to use the best-case combination within the given ranges to maximize profit. Final Answer: The maximum possible profit on eight books is Rs. 1800.

Question 4

The market price of an article is 40 percent more than its cost price. A customer initially receives a discount of 28.57 percent on the market price. Next day he returns and is given one more discount equal to 12.5 percent of the cost price due to a…

Accepted Answer

Introduction / Context: This profit and loss problem involves a marked price that is higher than the cost price, followed by two successive discounts. One discount is a relatively large percentage of the marked price, and the second discount is specified as a percentage of cost price. The aim is to compute the net profit or loss percentage after both discounts are given. Given Data / Assumptions: Cost price of the article = C. Market price (MP) = C increased by 40 percent, so MP = 1.40 * C. First discount on MP = 28.57 percent (approximately 2 / 7 of MP). Second discount given later = 12.5 percent of cost price C. Total discount is the sum of the first discount and this extra discount. Concept / Approach: To find overall gain or loss, we need the final selling price and compare it with cost price. The first discount is applied on the marked price, reducing it to a certain selling price. The extra discount is then given on top of this as a flat reduction equal to 12.5 percent of C. The combined effect gives a final selling price below or above C, which determines profit or loss percentage. Step-by-Step Solution: Assume cost price C = 100 units for convenience. Then market price MP = 1.40 * 100 = 140 units. First discount = 28.57 percent of MP ≈ 0.2857 * 140. Exact fraction is 2 / 7 of 140 = 40 units. So selling price after first discount = 140 - 40 = 100 units, which is equal to cost. Now an additional discount is given equal to 12.5 percent of cost price. 12.5 percent of C = 12.5 percent of 100 = 12.5 units. Final selling price = 100 - 12.5 = 87.5 units. Loss per article = cost price - final selling price = 100 - 87.5 = 12.5 units. Loss percent = 12.5 / 100 * 100 = 12.5 percent loss. Verification / Alternative check: Working directly from cost price: after first discount, the seller just breaks even because selling price becomes equal to cost price. Any further discount below that level will necessarily cause a loss. Since the second discount is exactly 12.5 percent of cost price, the resulting loss must also be 12.5 percent of cost price. This reasoning confirms the calculation. Why Other Options Are Wrong: Profit of 12.5% or 22.5%: These options assume that discounts still leave the selling price above cost, which is not possible once a further reduction below the break even point is made. Loss of 24.5%: This exaggerates the effect of the extra discount and does not match the actual arithmetic. Only a loss of 12.5 percent matches the correct computation. Common Pitfalls: Some candidates mistakenly think both discounts are applied on the marked price completely independently. Others ignore the fact that the second discount is specified in terms of cost price, not market price or previous selling price. Clear identification of the base values for each discount is crucial in mixed discount problems. Final Answer: The seller incurs an overall loss of about 12.5% on the article.

Question 5

The marked price of an article is increased by 25 percent and its selling price is increased by 16.66 percent. As a result, the amount of profit doubles. If the original marked price was Rs. 400 and this marked price was 33.33 percent above the corr…

Accepted Answer

Introduction / Context: This question combines markup, selling price changes, and profit calculations. It tells us that after increasing both the marked price and selling price by given percentages, the monetary profit doubles. Using the original relationship between cost price and marked price, we can determine the original selling price, then calculate the new selling price after the increase. Given Data / Assumptions: Original marked price MP0 = Rs. 400. Original marked price is 33.33 percent above cost price. Marked price is increased by 25 percent to a new marked price MP1. Selling price is increased by 16.66 percent to a new selling price SP1. The amount of profit doubles when going from original selling price SP0 to new selling price SP1. We must find SP1, the increased selling price. Concept / Approach: First determine the cost price using the given markup over cost. Then represent the original selling price as SP0 and write the profit as SP0 minus cost price. Next, the new selling price SP1 is 16.66 percent higher than SP0, so SP1 equals SP0 multiplied by a factor of approximately 7 / 6. The profit after the increase is SP1 minus cost price. The condition that profit doubles allows us to form an equation in SP0, which we can solve to get SP0 and then SP1. Step-by-Step Solution: Let the cost price be C. Original marked price MP0 = 400, which is 33.33 percent above cost. Thus 400 = C * (1 + 1 / 3) = (4 / 3) * C. So C = 400 * 3 / 4 = 300 rupees. Let SP0 be the original selling price. Original profit = SP0 - 300. New selling price SP1 is 16.66 percent greater than SP0. 16.66 percent is approximately 1 / 6, so SP1 = SP0 * (1 + 1 / 6) = (7 / 6) * SP0. New profit = SP1 - 300 = (7 / 6) * SP0 - 300. Given that new profit is double original profit: (7 / 6) * SP0 - 300 = 2 * (SP0 - 300). Multiply both sides to clear fraction: 7 * SP0 - 1800 = 12 * SP0 - 3600. Rearrange: 12 * SP0 - 7 * SP0 = 3600 - 1800. 5 * SP0 = 1800, so SP0 = 360 rupees. Therefore SP1 = (7 / 6) * 360 = 420 rupees. Verification / Alternative check: Original profit = SP0 - cost = 360 - 300 = 60 rupees. New profit = SP1 - cost = 420 - 300 = 120 rupees. The profit amount has doubled from Rs. 60 to Rs. 120 as required, so the new selling price of Rs. 420 is correct. Why Other Options Are Wrong: Rs. 380, Rs. 440, Rs. 460: These selling prices do not produce exactly double the original profit when checked against the cost price of Rs. 300. Only Rs. 420 satisfies both the profit doubling condition and the given selling price increase of 16.66 percent. Common Pitfalls: Some candidates mistakenly apply the 25 percent increase in marked price directly to selling price or assume that original selling price equals original marked price. Others misinterpret 16.66 percent and use approximate values in a way that changes the result. Working with simple rational equivalents like 1 / 6 for 16.66 percent helps to keep calculations clear and exact. Final Answer: The increased selling price of the article is Rs. 420.

Question 6

Every year before the festive season, a brand store increases the price of a product by 42 percent and then offers two successive discounts of 10 percent and 11 percent, respectively. What is the overall percentage gain or loss for the store on that…

Accepted Answer

Introduction / Context: This question examines the combined effect of a price hike followed by successive discounts. It is a classic example of successive percentage changes where the order of operations matters. The aim is to see whether these changes result in an overall profit or loss compared to the original cost price. Given Data / Assumptions: Original cost price of the product = C. Before the festive season, the price is increased by 42 percent. Two successive discounts are then given: first 10 percent, then 11 percent. We must compute the net percentage gain or loss relative to the original cost price. Concept / Approach: Successive percentage changes are handled by multiplying factors rather than adding or subtracting percentages directly. First we increase the cost by 42 percent to get a new marked price. Then we apply a 10 percent discount on this increased price, followed by an 11 percent discount on the already reduced price. The final selling price is compared to the original cost price to determine net gain or loss percentage. Step-by-Step Solution: Assume cost price C = 100 units for convenience. After 42 percent increase, marked price MP = 100 * 1.42 = 142 units. First discount of 10 percent: selling price after first discount = 142 * 0.90 = 127.8 units. Second discount of 11 percent on this new price: final selling price SP = 127.8 * 0.89. Calculate SP = 127.8 * 0.89 = 113.742 units. Net change compared with cost price 100 = 113.742 - 100 = 13.742 units. Percentage gain = 13.742 / 100 * 100 = 13.742 percent gain. Verification / Alternative check: We can also express the entire sequence as a single multiplicative factor on cost price. Overall factor = 1.42 (increase) * 0.90 (first discount) * 0.89 (second discount). That product is 1.42 * 0.90 * 0.89 = 1.13742 approximately, which means the final selling price is 1.13742 times the original cost. Therefore the net gain is about 13.742 percent, the same as obtained by direct calculation. Why Other Options Are Wrong: 3.25% loss or 13.742% loss: These assume the final price fell below cost, which is incorrect because the overall multiplicative factor is greater than 1. 3.25% gain: This underestimates the effect of the initial 42 percent price increase. Only a 13.742 percent gain matches the precise net effect of all the changes. Common Pitfalls: A frequent error is to subtract discounts directly from the 42 percent increase, such as 42 - 10 - 11, which ignores the multiplicative nature of successive percentage changes. Another mistake is to apply both discounts directly to the original cost rather than to the updated selling price after each step. Always convert each percentage change into a factor and multiply them in the correct order. Final Answer: The store makes an overall gain of approximately 13.742% on the product.

Question 7

A supplier sells a set of cartridges to a newspaper publishing house for Rs. 1540 and earns a profit of 25 percent on the deal. What is the cost price of the cartridges for the supplier?

Accepted Answer

Introduction / Context: This is a direct profit percentage problem. The selling price and profit percent are known, and we need to find the cost price. Such questions test basic rearrangement of the profit formula and are frequently asked in entry level quantitative aptitude tests. Given Data / Assumptions: Selling price (SP) of the cartridges = Rs. 1540. Profit percentage = 25 percent. We must find the cost price (CP) for the supplier. Concept / Approach: Profit percent is defined as profit divided by cost price, multiplied by 100. When profit percent and selling price are known, we use the relationship SP = CP * (1 + profit percent / 100). Rearranging that gives CP = SP / (1 + profit percent / 100). This formula is the easiest way to move from selling price and profit percent back to cost price. Step-by-Step Solution: Let CP be the cost price. Given profit percent = 25 percent, so SP = CP * (1 + 25 / 100) = CP * 1.25. We know SP = 1540, so 1540 = 1.25 * CP. Therefore CP = 1540 / 1.25. Compute CP = 1540 / 1.25 = 1232 rupees. Verification / Alternative check: Check using CP = Rs. 1232. Profit at 25 percent = 1232 * 25 / 100 = 308 rupees. Selling price = CP + profit = 1232 + 308 = 1540 rupees. This matches the given selling price, so CP is correctly found. Why Other Options Are Wrong: Rs. 1100, Rs. 1440, and Rs. 1793.4: None of these values, when marked up by 25 percent, yield a selling price of 1540 rupees. These options reflect errors in dividing or misapplying the profit percentage formula. Common Pitfalls: Some candidates mistakenly compute profit as a percentage of selling price or directly multiply selling price by 0.75 instead of dividing by 1.25. While multiplying by 0.8 would be correct for 25 percent discount, for profit calculation from selling price you must divide by 1 plus the profit rate, not subtract the rate from 1. Final Answer: The cost price of the cartridges is Rs. 1232.

Question 8

While selling a router, a shopkeeper gives a discount of 15 percent on the marked price. If he instead gives a discount of 20 percent, his profit falls by Rs. 51. What is the original marked price of the router?

Accepted Answer

Introduction / Context: This question involves discounts, marked price, and the effect on profit. The shopkeeper changes the discount rate by 5 percentage points, which leads to a fixed change in profit. From the difference in profits we can determine the marked price, since cost price is constant and only the selling price changes. Given Data / Assumptions: Marked price of the router = M (unknown). First scenario: discount = 15 percent on M. Second scenario: discount = 20 percent on M. The difference in profit between the two scenarios = Rs. 51. Cost price is constant in both cases. Concept / Approach: Profit in each scenario is selling price minus cost price. When the discount on marked price increases from 15 percent to 20 percent, the selling price decreases. The difference in profits between the two scenarios equals the difference between the two selling prices because the cost price does not change. That gives a direct equation linking the marked price and the known profit difference. Step-by-Step Solution: Let the marked price be M rupees. Selling price with 15 percent discount: SP1 = M * (1 - 15 / 100) = 0.85 * M. Selling price with 20 percent discount: SP2 = M * (1 - 20 / 100) = 0.80 * M. Difference in selling prices = SP1 - SP2 = 0.85M - 0.80M = 0.05M. Given that this difference in selling prices equals the drop in profit, which is Rs. 51. Therefore 0.05M = 51. M = 51 / 0.05 = 1020 rupees. Verification / Alternative check: Marked price M = Rs. 1020. With 15 percent discount: SP1 = 1020 * 0.85 = Rs. 867. With 20 percent discount: SP2 = 1020 * 0.80 = Rs. 816. Difference in selling prices = 867 - 816 = Rs. 51. This matches the given difference in profit, so the marked price is correct. Why Other Options Are Wrong: Rs. 1000, Rs. 1040, and Rs. 980: For each of these marked prices, the difference between selling prices with 15 percent and 20 percent discounts would not be exactly Rs. 51. Only Rs. 1020 satisfies the condition that a 5 percentage point change in discount leads to a Rs. 51 change in profit. Common Pitfalls: Candidates sometimes incorrectly attempt to include cost price in the equation, even though it cancels out when taking the difference between profits. Another mistake is to treat the 5 percent as 5 rupees instead of 5 percent of the marked price. Always remember that percentage changes must be applied to the relevant base amount, here the marked price. Final Answer: The original marked price of the router is Rs. 1020.

Question 9

Rajan invests Rs. 1,00,000 in foreign stocks when the exchange rate is 75 rupees per unit of foreign currency. After one year, his investment grows by 20 percent in foreign currency terms. He then converts the full amount back to Indian rupees at an…

Accepted Answer

Introduction / Context: This question combines percentage returns on an investment with currency exchange rate fluctuations. It tests understanding of how investment growth in foreign currency and changes in the exchange rate together affect the final return when measured in domestic currency, here Indian rupees. Given Data / Assumptions: Initial investment in rupees = Rs. 1,00,000. Initial exchange rate = 75 rupees per unit of foreign currency. Investment grows by 20 percent in foreign currency terms after one year. Final exchange rate when converting back to rupees = 80 rupees per unit of foreign currency. We must find the overall gain or loss percentage in rupee terms. Concept / Approach: First convert the rupee investment into foreign currency units using the initial exchange rate. Then apply the 20 percent growth to find the final amount in foreign currency. Finally, convert that amount back to rupees using the new exchange rate. The change from the original rupee investment to the final rupee amount provides the net gain or loss percentage. This is essentially a product of an investment growth factor and a currency movement factor. Step-by-Step Solution: Initial rupee investment = 1,00,000. Initial exchange rate = 75 rupees per foreign unit. Foreign currency units purchased = 1,00,000 / 75. Compute this: 1,00,000 / 75 = 1333.333... units approximately. After 20 percent growth in foreign currency terms, foreign amount = 1333.333... * 1.20 = 1600 units. Final exchange rate = 80 rupees per foreign unit. Final rupee amount = 1600 * 80 = 1,28,000 rupees. Net gain in rupees = 1,28,000 - 1,00,000 = 28,000 rupees. Gain percentage = 28,000 / 1,00,000 * 100 = 28 percent. Verification / Alternative check: We can also see this as a combined multiplicative effect. The foreign investment grows by a factor of 1.20, while each foreign unit is now worth 80 / 75 times as many rupees due to the exchange rate change. Overall factor on rupees = 1.20 * (80 / 75) = 1.20 * 1.0666... ≈ 1.28. This is exactly a 28 percent gain, confirming the previous calculation. Why Other Options Are Wrong: Loss of 24% or loss of 28%: These would only occur if the currency movement or investment return were negative overall, which is not the case here. Gain of 20%: This ignores the additional positive effect of the currency appreciation from 75 to 80. Only a gain of 28 percent correctly combines both sources of increase. Common Pitfalls: Candidates may forget to account for the change in exchange rate and only calculate the 20 percent investment growth. Others may incorrectly treat the exchange rate change as a simple addition in percentages. Always convert to foreign currency, apply the investment growth, then convert back with the new rate to see the true effect in domestic currency. Final Answer: Rajan earns a real return of 28% in rupee terms.

Question 10

Rishi buys 30 kg of sugar at Rs. 9 per kg and 45 kg of sugar at Rs. 10 per kg. He mixes both types and sells the entire mixture at Rs. 9.75 per kg. What is his net gain or loss in rupees on the whole transaction?

Accepted Answer

Introduction / Context: This mixture problem tests the ability to compute weighted average cost price and compare it with a single selling price. Rishi mixes two types of sugar bought at different rates and sells at one uniform rate. The question is whether he gains or loses on the mixture and by how much in rupee terms. Given Data / Assumptions: First lot: 30 kg of sugar at Rs. 9 per kg. Second lot: 45 kg of sugar at Rs. 10 per kg. Selling price of the mixture = Rs. 9.75 per kg. All sugar bought is sold, and there is no wastage. Concept / Approach: First calculate the total cost of each lot and then add them to get the total cost of the entire mixture. Next, compute the total quantity of sugar and multiply by the selling price per kg to find the total revenue. The difference between total revenue and total cost gives the net gain or loss. This method is more reliable than trying to guess the average price directly. Step-by-Step Solution: Cost of first lot = 30 kg * Rs. 9 per kg = Rs. 270. Cost of second lot = 45 kg * Rs. 10 per kg = Rs. 450. Total cost = 270 + 450 = Rs. 720. Total quantity of sugar = 30 kg + 45 kg = 75 kg. Selling price per kg of mixture = Rs. 9.75. Total selling price = 75 kg * Rs. 9.75 per kg. Compute: 75 * 9.75 = 731.25 rupees. Net gain = total selling price - total cost = 731.25 - 720 = Rs. 11.25. Verification / Alternative check: We can also compute the average cost price per kg. Average CP per kg = total cost / total kg = 720 / 75 = Rs. 9.60 per kg. He sells at Rs. 9.75 per kg. Profit per kg = 9.75 - 9.60 = Rs. 0.15 per kg. On 75 kg, total profit = 75 * 0.15 = Rs. 11.25, which matches our earlier result. Why Other Options Are Wrong: Rs. 10.75, Rs. 12, and Rs. 13.50: These correspond to incorrect calculations of average cost or total selling price. Only Rs. 11.25 matches both the total cost comparison and the average cost approach. Common Pitfalls: A common mistake is to simply average the two prices (9 and 10) without weighting them by quantity. Another error is to forget to multiply by total kilograms when computing total selling price or to mis-handle decimal multiplication. Always compute total cost and total revenue carefully when working with mixtures. Final Answer: Rishi makes a net profit of Rs. 11.25 on the whole sugar mixture.

Question 11

The cost price of 40 magazines is equal to the selling price of P magazines of the same kind. If the profit made on the sale is 25 percent, what is the value of P?

Accepted Answer

Introduction / Context: This question evaluates understanding of the relationship between cost price and selling price when profit is given. It uses an equation linking the cost of several items to the selling price of a different number of items. The structure is similar to other standard profit percentage questions seen in competitive exams. Given Data / Assumptions: Cost price of 40 magazines together = total CP. Selling price of P magazines together = total SP. Total CP of 40 magazines = total SP of P magazines. Profit earned on each magazine is 25 percent. All magazines are identical, and cost price per magazine is constant. Concept / Approach: We use variables to represent cost price per magazine and selling price per magazine. The given profit percentage helps us express selling price in terms of cost price. Equating total cost of 40 magazines with total selling price of P magazines yields an equation that can be solved for P. Step-by-Step Solution: Let cost price of one magazine be C. Then total cost price of 40 magazines = 40 * C. Given profit percent = 25 percent, so selling price of one magazine S = C * (1 + 25 / 100) = 1.25 * C. Total selling price of P magazines = P * S = P * 1.25 * C. Given: 40 * C = P * 1.25 * C. Divide both sides by C (C is not zero): 40 = 1.25 * P. So P = 40 / 1.25 = 32. Verification / Alternative check: Assume C = Rs. 100 for easy verification. Cost of 40 magazines = 40 * 100 = Rs. 4000. Selling price per magazine with 25 percent profit = 100 * 1.25 = Rs. 125. If P = 32, total selling price of 32 magazines = 32 * 125 = Rs. 4000. This equals the total cost of 40 magazines, confirming that P = 32 is correct. Why Other Options Are Wrong: 40: This would imply no profit and contradict the 25 percent profit condition. 16 and 30: These values do not satisfy the equation 40 = 1.25 * P. Only P = 32 balances total cost price and total selling price correctly under a 25 percent profit. Common Pitfalls: A typical mistake is to mix up cost price and selling price or to ignore the profit percentage when forming the equation. Some candidates also attempt to use trial and error instead of using a clear algebraic relationship. Writing down the equation 40 * C = P * 1.25 * C helps avoid such confusion. Final Answer: The value of P is 32.

Question 12

A wholesale dealer allows a discount of 20 percent on the marked price to the retailer. The retailer then sells the article at 5 percent below the marked price to the final customer. If the customer pays Rs. 19 for the article, what is the retailer'…

Accepted Answer

Introduction / Context: This question explores the profit made by a retailer who buys goods from a wholesaler at a discount on the marked price and then sells the same goods at another price to the final customer. The goal is to identify the retailer's cost price and selling price, and then compute the profit in rupees. Given Data / Assumptions: Marked price of the article = M (unknown). Wholesale dealer gives retailer a discount of 20 percent on M. Retailer sells to customer at 5 percent below M, that is at 95 percent of M. The customer pays Rs. 19 for the article, which is this final selling price. We must find the retailer's profit in rupees. Concept / Approach: The retailer's cost price is the price he pays to the wholesaler, which is the marked price less 20 percent. His selling price is the price at which he sells to the customer, which is 5 percent less than the marked price. By expressing both cost price and selling price in terms of M, and then using the fact that the selling price equals Rs. 19, we can determine M and hence compute the profit as selling price minus cost price. Step-by-Step Solution: Let the marked price be M rupees. Retailer buys from wholesaler at 20 percent discount: cost price for retailer = M * (1 - 20 / 100) = 0.80 * M. Retailer sells to customer at 5 percent below marked price: selling price = M * (1 - 5 / 100) = 0.95 * M. Given final selling price to customer = 19 rupees. So 0.95 * M = 19, hence M = 19 / 0.95 = 20 rupees. Retailer's cost price = 0.80 * 20 = 16 rupees. Retailer's selling price = 19 rupees. Retailer's profit = selling price - cost price = 19 - 16 = 3 rupees. Verification / Alternative check: To check, we can recalculate from the determined marked price. Marked price M = 20 rupees. The wholesaler gives 20 percent discount, so the retailer pays 20 * 0.80 = 16 rupees. Retailer charges the customer 5 percent less than 20, that is 20 * 0.95 = 19 rupees. The customer indeed pays 19 and retailer gains 3 rupees, consistent with the information given. Why Other Options Are Wrong: Rs. 4 and Rs. 5: These profits would require different relationships between marked price and discounts, which do not match the actual calculations. Rs. 1: This underestimates the profit and arises from miscalculating the retailer's cost or the customer's payment. Only Rs. 3 is consistent with the computed cost and selling prices. Common Pitfalls: Some candidates confuse the discount given by the wholesaler with the discount given by the retailer and mistakenly combine them directly. Others misidentify the base on which each percentage is applied. The wholesaler's discount is on marked price when selling to the retailer, and the retailer's discount is also on marked price when selling to the customer. Keeping these roles clear is essential for correct calculation. Final Answer: The retailer makes a profit of Rs. 3 on the article.

Question 13

A shopkeeper sells two different articles for Rs. 1000 each. On the first article he makes a profit of 30 percent and on the second article he incurs a loss of 20 percent. What is the net percentage profit or loss over both articles taken together?

Accepted Answer

Introduction / Context:This profit and loss question checks how to combine gains and losses over two items when the selling prices are equal. Many learners make the mistake of simply averaging the percentage values, which gives an incorrect result. Instead, we must work with the actual cost prices and selling prices to obtain the true net percentage profit or loss. Given Data / Assumptions: First article is sold for Rs. 1000 with a profit of 30 percent. Second article is sold for Rs. 1000 with a loss of 20 percent. We assume normal profit and loss definitions based on cost price. We need the net percentage profit or loss over both articles together. Concept / Approach:The key idea is that percentage profit or loss is always calculated on cost price. When different percentage changes are applied, we must compute the individual cost prices from the given selling prices. Then we add total cost price and total selling price and finally compute the overall percentage change by using the standard formula: percentage profit or loss equals (total selling price minus total cost price) divided by total cost price, multiplied by 100. Step-by-Step Solution:Let the selling price of each article be 1000 rupees.For the first article, profit is 30 percent, so cost price one equals 1000 / 1.30 which is approximately 769.23 rupees.For the second article, loss is 20 percent, so 1000 equals 80 percent of cost price two. Therefore, cost price two equals 1000 / 0.80 which is 1250 rupees.Total cost price equals 769.23 plus 1250 which is 2019.23 rupees approximately.Total selling price equals 1000 plus 1000 which is 2000 rupees.Net loss equals total cost price minus total selling price, which is about 19.23 rupees.Percentage loss equals 19.23 / 2019.23 * 100 which is about 0.95 percent. Verification / Alternative check:As an approximate check, note that the first article was bought very cheaply compared to 1000 and the second article was bought at a much higher cost. The second cost price is 1250, so the second sale causes a significant rupee loss. When both are added, the total selling price of 2000 is slightly less than the combined cost price of a little over 2019. The difference is clearly very small compared to two thousand, so a loss below one percent is reasonable. This qualitative reasoning supports the detailed calculation that produced a loss close to 0.95 percent. Why Other Options Are Wrong:Option 0.85 percent loss is smaller in magnitude than the correct value and does not match the computed ratio of loss to total cost. Option 1.00 percent loss is slightly larger than the correct answer and would require a little more rupee loss than actually occurs here. Option 1.30 percent loss is even larger and clearly exaggerates the loss compared to the actual difference of about 19.23 rupees on a cost of just over two thousand rupees. Common Pitfalls:A very common mistake is to average the percentages and say that the shopkeeper has (30 minus 20) divided by 2 equals 5 percent profit, which is completely incorrect. Another mistake is to average directly as (30 minus 20) equals 10 percent profit, ignoring that one percentage is profit and the other is loss. Students also sometimes calculate percentages on the selling price rather than on the cost price, which again leads to wrong results. Always compute exact cost prices for each item and then combine them to find the true overall profit or loss. Final Answer:The shopkeeper makes a very small overall loss, and the correct net result is a 0.95 percent loss on the combined transaction.

Question 14

Watson buys a book for Rs. 240 and sells it to Johny at a profit of 50 percent. Johny wants to sell the same book to Shekar so that he earns a profit of 25 percent, but Shekar insists on buying it at a discount of 10 percent on the marked price. Wha…

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Introduction / Context:This problem combines successive profits and a discount, a common pattern in profit and loss aptitude questions. First one person makes a profit and sells to another, and then the second person wants a further profit while giving a discount to the final buyer. The question asks for the marked price that allows the second person to keep a desired profit percentage despite allowing a discount. Given Data / Assumptions: Watson buys the book for Rs. 240. Watson sells it to Johny at a profit of 50 percent. Johny wants a profit of 25 percent on his own cost price. Shekar will buy only if he gets a discount of 10 percent on the marked price. We must find the marked price that Johny should quote. Concept / Approach:We need to move step by step through the chain of transactions. First, we calculate Johny cost price from Watson selling price. Next, we find the selling price that gives Johny a 25 percent profit. Finally, we relate that selling price to the marked price after providing a 10 percent discount. Throughout, we use the basic profit formula: selling price equals cost price multiplied by (1 plus profit percentage divided by 100). For discounts, selling price equals marked price multiplied by (1 minus discount percentage divided by 100). Step-by-Step Solution:Watson cost price is 240 rupees.Watson sells with a profit of 50 percent, so his selling price equals 240 * 1.50 which is 360 rupees.Therefore, Johny cost price is 360 rupees.Johny wants a profit of 25 percent on his cost, so required selling price equals 360 * 1.25 which is 450 rupees.Shekar receives a discount of 10 percent on the marked price, so actual selling price equals 90 percent of the marked price.Let marked price be M, then 0.90 * M equals 450.Therefore M equals 450 / 0.90 which is 500 rupees. Verification / Alternative check:We can quickly verify the result. If Johny marks the price at 500 rupees and gives a 10 percent discount, the sale happens at 500 * 0.90 equals 450 rupees. His cost price is 360 rupees, so his profit is 450 minus 360 equals 90 rupees. Percentage profit equals 90 / 360 * 100 which is exactly 25 percent, matching the requirement. This confirms that our calculations are consistent at every stage of the transaction chain. Why Other Options Are Wrong:Option 450 rupees would become 405 rupees after a 10 percent discount, giving Johny a profit of only 45 rupees, which is 12.5 percent, not 25 percent. Option 360 rupees would give a selling price of 324 rupees after discount, which is even below Johny cost price, leading to a loss. Option 415 rupees would give a selling price of 373.5 rupees, which yields a profit of only 13.75 rupees, again far below 25 percent. Only 500 rupees satisfies the discount and profit conditions together. Common Pitfalls:A common mistake is to apply the 25 percent profit directly on Watson original cost instead of on Johny cost, which changes the base. Another mistake is to ignore the discount and simply increase the price by 25 percent, which does not ensure that the final discounted selling price gives the desired profit. Some learners also confuse marked price with selling price. Remember that the discount applies on the marked price and the profit is always computed on cost price. Final Answer:Johny should mark the book at Rs. 500 in order to give a 10 percent discount and still earn a 25 percent profit.

Question 15

A person steals Rs. 100 from a store without the owner noticing. Later he returns to the same store and uses that stolen Rs. 100 note to buy goods worth Rs. 60, receiving Rs. 40 back as change. Considering both the theft and the purchase together, h…

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Introduction / Context:This is a popular logical profit and loss puzzle. Instead of simple percentage calculations, it tests whether you understand how cash and goods move between the thief and the store owner. The key is to track what the owner finally loses in both money and goods after the entire sequence of events, not just the initial theft. Given Data / Assumptions: A person steals Rs. 100 from a store. Later he buys goods worth Rs. 60 using the same stolen Rs. 100 note. The store owner gives him Rs. 40 as change. We assume there are no other transactions or recoveries. We must find the net loss to the store owner. Concept / Approach:We analyse the transaction in two parts. First is the theft, where the thief takes money without giving anything in return. Second is the later purchase, where the thief uses stolen money to buy goods and receive change. We must consider the store owner point of view: how much cash and how much stock leave the store, and how much real value comes back. It helps to classify the flows as loss of cash and loss of goods, then add them. Step-by-Step Solution:When the person steals Rs. 100, the store loses Rs. 100 in cash immediately.Later, the thief returns and uses this same Rs. 100 note to buy goods worth Rs. 60.From the store perspective, the Rs. 100 that it receives is actually its own money returning, not new income.In the purchase, the store gives away goods worth Rs. 60 and also gives Rs. 40 as change.Therefore, during the purchase, the store loses goods worth Rs. 60 plus Rs. 40 in additional cash, totalling Rs. 100.Combined with the original loss, the net loss in goods and cash is Rs. 100 from the theft plus Rs. 60 in goods plus Rs. 40 in cash.However, the Rs. 100 note returned during the purchase cancels the initial cash loss, so we track final position: only goods worth 60 and cash of 40 are gone.Hence the final effective loss is 60 plus 40 equals 160 rupees. Verification / Alternative check:Think of the thief as walking away finally with two things: goods worth Rs. 60 and cash worth Rs. 40. That total benefit to the thief is Rs. 100 in value. All of this value must have come from the store, because the thief had no genuine money of his own in the whole process. Therefore, the store must have lost Rs. 160 in total. This alternative viewpoint confirms the earlier calculation, because the store wealth decreases by exactly the amount of cash and goods that the thief ultimately possesses. Why Other Options Are Wrong:Option 200 rupees counts the original stolen 100 rupees and the later 60 plus 40 again without cancelling the return of the stolen note. Option 100 rupees considers only the value of the goods or only the initial theft but not the change in both steps. Option 40 rupees is clearly too low because the store lost more than just the change; it also lost goods. Only the value of 160 rupees correctly represents the store final loss in cash and goods together. Common Pitfalls:Many learners double count the stolen 100 rupees or forget that when the thief pays with the stolen note, the store is simply getting its own money back. Others focus only on the goods worth Rs. 60 and ignore the extra cash of Rs. 40 given as change. The safest method is to analyse the final situation: how much value is in the thief hands and how much has left the store. That complete view avoids the confusion caused by intermediate exchanges of the same note. Final Answer:The store owner total loss, combining goods and cash, is Rs. 160.

Question 16

A man buys a trouser for Rs. 1250. If he gets a reduction of 20 percent in the price of the trouser, he can use the remaining money to buy a t shirt as well, so that the total spending stays equal to the original Rs. 1250. What is the price of the t…

Accepted Answer

Introduction / Context:This problem is a straightforward application of percentage reduction and basic arithmetic. The buyer first considers a single item, then a discounted price allows him to buy an additional item while keeping the total expenditure unchanged. The goal is to use the information about the discount to find the price of the second item. Given Data / Assumptions: The man buys a trouser for Rs. 1250 initially. The price of the trouser is reduced by 20 percent. Using the reduced price, he can buy both the trouser and a t shirt for a total of Rs. 1250. We assume there are no other taxes or discounts. We need to find the price of the t shirt. Concept / Approach:The key concept is that a percentage reduction decreases the price by a certain fraction of the original price. Here a 20 percent reduction means the new price is 80 percent of the original price. Once we compute the reduced trouser price, we subtract that amount from the fixed budget of Rs. 1250. The remaining amount must be the cost of the t shirt. The entire calculation only uses simple multiplication and subtraction. Step-by-Step Solution:Original price of the trouser equals 1250 rupees.Reduction is 20 percent, which means the new price is 80 percent of 1250.Compute reduced trouser price as 1250 * 0.80 which is 1000 rupees.The man total budget remains 1250 rupees, the same as the original price of the trouser.After buying the trouser at the reduced price of 1000 rupees, the remaining money is 1250 minus 1000 which is 250 rupees.This remaining amount must be the price of the t shirt. Verification / Alternative check:We can verify the solution by checking the total expenditure after the reduction. If the trouser costs 1000 rupees and the t shirt costs 250 rupees, then the total amount spent is 1000 plus 250 which equals 1250 rupees. This matches the original single purchase amount, so the condition in the problem is satisfied exactly. Therefore the derived t shirt price is consistent with all the given information. Why Other Options Are Wrong:If the t shirt cost 125 rupees, the total spending would be 1000 plus 125 equals 1125 rupees, which is less than 1250 rupees. For 225 rupees, the total would be 1225 rupees, still less than the original amount. For 200 rupees, the total would be 1200 rupees. None of these totals matches the requirement that the combined cost equals the original trouser price of 1250 rupees. Only 250 rupees makes the total exactly 1250 rupees. Common Pitfalls:Some learners mistakenly subtract 20 rupees instead of 20 percent, which is incorrect because the reduction is a percentage of the original price, not a fixed rupee amount. Others forget that the full original amount is available to buy both items and treat the reduced trouser price as the total budget. Carefully reading the statement about spending the same amount as before is essential to set up the correct equation. Final Answer:The price of the t shirt that can be purchased along with the discounted trouser is Rs. 250.

Question 17

By selling 90 pens for Rs. 80 a man incurs a loss of 20 percent on the transaction. At what selling price in rupees should he sell the same 90 pens in order to make a profit of 20 percent instead?

Accepted Answer

Introduction / Context:This question is a classic example of converting a loss making sale into a profitable one using percentage profit and loss concepts. The seller knows the total selling price at which he suffers a loss and the percentage loss. From that, we can find the total cost price. Once the cost price is known, we can compute the new selling price that would yield a desired profit percentage on the same quantity. Given Data / Assumptions: He sells 90 pens for Rs. 80 and incurs a loss of 20 percent. The loss percentage is computed on cost price as usual. The quantity in the second case remains 90 pens. He wants a profit of 20 percent on the same total cost price. We must find the new total selling price for 90 pens. Concept / Approach:We first use the loss formula. When there is a 20 percent loss, the selling price equals 80 percent of the cost price. Hence, total cost price equals selling price divided by 0.80. Once we know the total cost price for 90 pens, we use the profit formula. For a 20 percent profit, selling price equals cost price multiplied by 1.20. Since the number of pens is unchanged, there is no need to work on a per pen basis; all calculations can be done on the total amounts. Step-by-Step Solution:Total selling price for 90 pens in the first case is 80 rupees.Loss is 20 percent, so selling price equals 80 percent of cost price.Let total cost price be C. Then 0.80 * C equals 80.Therefore, C equals 80 / 0.80 which is 100 rupees.For a 20 percent profit, the new selling price S must be 1.20 times the cost price.So S equals 1.20 * 100 which is 120 rupees.Hence, the 90 pens must be sold for 120 rupees in total to earn a 20 percent profit. Verification / Alternative check:We can check our answer by computing percentage profit. At the new selling price of 120 rupees, profit equals 120 minus 100 equals 20 rupees. The percentage profit is 20 divided by 100 multiplied by 100, which is exactly 20 percent. This matches the requirement in the question, so the computed selling price is correct. The arithmetic is simple and consistent with standard percentage formulas. Why Other Options Are Wrong:If he sells for 90 rupees, his profit would be 90 minus 100 which is negative 10, a loss of 10 percent. For 100 rupees, there would be neither profit nor loss. For 110 rupees, the profit of 10 rupees on a cost of 100 is only 10 percent. None of these options meet the target profit of 20 percent. Only 120 rupees gives the correct profit percentage. Common Pitfalls:Some learners mistakenly use the 20 percent on the selling price to recover cost price, which is incorrect because profit and loss percentages are always based on cost price. Others may try to adjust the selling price directly by adding 40 percent to 80 rupees, forgetting that the base amount for the profit calculation is the cost price, not the earlier selling price. Always identify clearly which value the percentage refers to before performing calculations. Final Answer:The man should sell the 90 pens for a total of Rs. 120 to earn a 20 percent profit.

Question 18

A trader mixes 36 kilograms of rice priced at Rs. 20 per kilogram with 14 kilograms of another variety of rice priced at Rs. 36 per kilogram. He sells the mixed rice at Rs. 30 per kilogram. What percentage profit does he make on the overall transact…

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Introduction / Context:This is a mixture and profit question involving two types of rice with different cost prices. The trader mixes them in given quantities and then sells the mixture at a single uniform price per kilogram. The problem checks whether you can compute the total cost price, total selling price, and then derive the overall percentage profit on the combined quantity. Given Data / Assumptions: First variety of rice: 36 kilograms at Rs. 20 per kilogram. Second variety of rice: 14 kilograms at Rs. 36 per kilogram. Total mixture is sold at Rs. 30 per kilogram. There is no loss of weight during mixing or selling. We must find the trader profit percentage on the entire transaction. Concept / Approach:The correct method is to compute the total cost of each component and sum them to get the overall cost price of the mixture. Then we compute the total selling price by multiplying the selling rate by the total quantity in kilograms. After that, profit equals total selling price minus total cost price. Finally, percentage profit equals profit divided by total cost price multiplied by 100. There is no need for alligation formula here, though it could also be used as an alternative approach. Step-by-Step Solution:Total quantity of rice equals 36 plus 14 which is 50 kilograms.Cost of first variety equals 36 * 20 which is 720 rupees.Cost of second variety equals 14 * 36 which is 504 rupees.Total cost price equals 720 plus 504 which is 1224 rupees.Selling price per kilogram is 30 rupees.Total selling price equals 50 * 30 which is 1500 rupees.Profit equals 1500 minus 1224 which is 276 rupees.Percentage profit equals 276 / 1224 * 100 which is approximately 22.54 percent. Verification / Alternative check:We can compute the average cost price per kilogram of the mixture by dividing total cost by total quantity. That gives 1224 divided by 50 which is 24.48 rupees per kilogram approximately. The selling price per kilogram is 30 rupees. The profit per kilogram is therefore 30 minus 24.48 which is 5.52 rupees. The percentage profit per kilogram equals 5.52 / 24.48 * 100 which again gives about 22.54 percent. This confirms that the detailed total calculation is consistent with the average price approach. Why Other Options Are Wrong:Option 25 percent would require a higher profit or a lower cost price than actually present in the data. Option 21.14 percent and option 27.32 percent do not match the computed ratio of profit to total cost. They may result from common calculator errors or incorrect use of approximate values. Only 22.54 percent matches the exact calculation derived from the given quantities and prices. Common Pitfalls:Some learners mistakenly average the two prices 20 and 36 directly, ignoring the different quantities. Others compute percentage profit based on one component only or mix up per kilogram profit and overall profit. Always remember that when quantities differ, you must use weighted averages or work with full totals for cost and selling price. Careful attention to multiplication and addition avoids most mistakes in such mixture problems. Final Answer:The trader makes a profit of approximately 22.54 percent on the mixed rice.

Question 19

Watches are bought at prices ranging from Rs. 200 to Rs. 350 and sold at prices ranging from Rs. 300 to Rs. 425. What is the greatest possible total profit in rupees that can be made by selling nine watches under these conditions?

Accepted Answer

Introduction / Context:This question is about maximizing profit when there is a permitted range for buying and selling prices. It is a simple optimization problem that does not require percentages. Instead, we use the idea that maximum profit is obtained by buying at the lowest possible cost and selling at the highest possible price within the given ranges for each item. Given Data / Assumptions: Each watch can be bought for any price between Rs. 200 and Rs. 350. Each watch can be sold for any price between Rs. 300 and Rs. 425. There are nine watches in total. We assume that it is possible to buy each watch at the minimum allowed cost and sell each at the maximum allowed price. We must find the maximum total profit over all nine watches. Concept / Approach:To maximize profit, the trader must minimize cost and maximize selling price per watch. Therefore, he will buy each watch at the lowest price in the allowed range and sell each at the highest price in the allowed range. The profit per watch will be the difference between the highest selling price and the lowest cost price. The total profit is then this difference multiplied by the total number of watches, which is nine. Step-by-Step Solution:Minimum possible cost price per watch equals 200 rupees.Maximum possible selling price per watch equals 425 rupees.Maximum profit per watch equals 425 minus 200 equals 225 rupees.There are nine watches in total.Therefore, maximum total profit equals 225 multiplied by 9.225 * 9 equals 2025 rupees. Verification / Alternative check:We can verify logically that there is no better strategy. Any increase in cost above 200 rupees reduces profit directly. Any decrease in selling price below 425 rupees also reduces profit. Since the ranges are inclusive and we are allowed to choose any value within them, taking the extremes gives the maximum difference between selling price and cost price. Multiplying that difference by the number of identical items gives the maximum total profit. Why Other Options Are Wrong:Option 1800 rupees corresponds to a smaller per watch profit and would assume either a higher cost price than 200 or a lower selling price than 425. Option 2000 rupees is not an exact multiple of 9 given the 225 rupee per watch gap, and does not match the precise calculation. Option 1750 rupees also does not correspond to any consistent choice of minimum cost and maximum selling price. Only 2025 rupees matches the optimal difference multiplied by nine watches. Common Pitfalls:Some learners mistakenly average the buying and selling ranges and multiply the difference of averages by nine, which gives a smaller profit. Others assume the same fixed price for all watches without using the extremes of the range. Always remember that when the goal is to maximize profit under such flexible conditions, the best strategy is to buy as low as allowed and sell as high as allowed for every item. Final Answer:The greatest possible total profit on nine watches is Rs. 2025.

Question 20

A shopkeeper who deals in books sells a book at a loss of 16 percent. If she had charged an additional Rs. 60 on the selling price, she would have made a profit of 14 percent instead. What is the cost price of the book in rupees?

Accepted Answer

Introduction / Context:This is a classic profit and loss question involving two scenarios with the same cost price but different selling prices. In the first case there is a loss, and in the second case there is a profit after increasing the selling price by a fixed rupee amount. The task is to find the original cost price of the book using these two percentage conditions. Given Data / Assumptions: In the first scenario, the book is sold at a loss of 16 percent. If the selling price is increased by Rs. 60, then there is a profit of 14 percent. The cost price of the book remains the same in both scenarios. We ignore any taxes or additional charges. We must determine the cost price in rupees. Concept / Approach:Let the cost price of the book be C. A loss of 16 percent means the selling price equals 84 percent of C. A profit of 14 percent means the selling price equals 114 percent of C. The second selling price is exactly Rs. 60 more than the first. Therefore, we can set up an equation connecting these two selling prices and C, and then solve for C using simple algebra. Step-by-Step Solution:Let cost price C be an unknown value in rupees.Selling price in the loss case is 84 percent of C, so S1 equals 0.84 * C.Selling price in the profit case is 114 percent of C, so S2 equals 1.14 * C.We are told that S2 is 60 rupees more than S1.Therefore, 1.14 * C equals 0.84 * C plus 60.Subtract 0.84 * C from both sides to get 0.30 * C equals 60.Hence C equals 60 divided by 0.30, which is 200 rupees. Verification / Alternative check:We can verify by computing both selling prices using C equals 200. With a 16 percent loss, S1 equals 200 * 0.84 which is 168 rupees. With a 14 percent profit, S2 equals 200 * 1.14 which is 228 rupees. The difference S2 minus S1 equals 228 minus 168 which is exactly 60 rupees, matching the problem statement. This confirms that C equals 200 rupees is consistent with both scenarios and the given increase in selling price. Why Other Options Are Wrong:If we take C as 185, 16 percent loss gives 155.4 and 14 percent profit gives 210.9, whose difference is not 60 rupees. For 154, the corresponding selling prices also do not differ by 60 rupees. For 177, the gap between loss selling price and profit selling price again does not match the required difference. Only 200 rupees produces selling prices that differ by exactly 60 rupees while matching both percentage conditions. Common Pitfalls:Some learners incorrectly assume that 16 percent and 14 percent sum directly to form a 30 percent gap in selling prices, which is not true because percentages are applied on the same cost price, not directly added on selling price. Others misinterpret which percentage corresponds to loss and which to profit, leading to a wrong equation. Working step by step and writing each selling price formula explicitly avoids these errors. Final Answer:The correct cost price of the book is Rs. 200.

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