Question 1

Selling a coat at Rs 1425 yields a gain that is 6% more than the gain when selling it at Rs 1353. Find the cost price of the coat.

Accepted Answer

Introduction:Two selling prices produce gains that differ by 6 percentage points. Express gains relative to the unknown cost price (CP) and equate the difference to 6%. Given Data / Assumptions: SP1 = Rs 1425, SP2 = Rs 1353 Gain% at SP1 is 6 percentage points more than at SP2 Concept / Approach:Gain% = (SP − CP)/CP. Difference: [(1425 − CP)/CP] − [(1353 − CP)/CP] = 0.06. Step-by-Step Solution:[(1425 − CP) − (1353 − CP)] / CP = 0.06(72) / CP = 0.06 ⇒ CP = 72 / 0.06 = 1200 Verification / Alternative check:Gain% at 1353: (1353 − 1200)/1200 = 12.75%. At 1425: (1425 − 1200)/1200 = 18.75%. Difference = 6%. Why Other Options Are Wrong:1000, 1250, 1500: Do not produce a 6% difference with the given SPs. Common Pitfalls:Using 6% of SP instead of 6 percentage points of gain on CP. Final Answer:Rs. 1200

Question 2

A person sells two cows at Rs 9900 each. He gains 10% on one and loses 20% on the other. Determine the overall result.

Accepted Answer

Introduction:Selling two items at the same price with unequal gain and loss generally yields a net loss when the loss percentage exceeds the gain percentage. Compute exact CPs and compare with total SP. Given Data / Assumptions: SP1 = Rs 9900 with 10% gain SP2 = Rs 9900 with 20% loss Concept / Approach:Find CP1 and CP2 using SP = (1 ± rate)*CP, then compare total SP and total CP. Step-by-Step Solution:For 10% gain: 9900 = 1.10 * CP1 ⇒ CP1 = 9000For 20% loss: 9900 = 0.80 * CP2 ⇒ CP2 = 12375Total CP = 9000 + 12375 = 21375Total SP = 9900 + 9900 = 19800Net result = 19800 − 21375 = −1575 (loss of Rs 1575) Verification / Alternative check:Percentage analysis confirms that a 20% loss outweighs a 10% gain when prices are equalized. Why Other Options Are Wrong:He gained Rs. 200 / lost Rs 200 / neither: All contradict the computed loss of Rs 1575. Common Pitfalls:Assuming gains and losses cancel because selling prices are equal; ignoring the CP base effect. Final Answer:None of the above

Question 3

An item costs Rs 200 and is sold at a 10% loss. If the price is further reduced by 5 percentage points, what is the new selling price?

Accepted Answer

Introduction:Loss percentages are on cost price (CP). If the loss increases from 10% to 15%, compute the new SP as (1 − 0.15)*CP. Given Data / Assumptions: CP = Rs 200 Initial loss = 10% ⇒ SP1 = 0.90 * 200 = 180 Further reduction by 5 percentage points ⇒ total loss = 15% Concept / Approach:New SP = (1 − 0.15) * 200 = 0.85 * 200. Step-by-Step Solution:SP2 = 0.85 * 200 = Rs 170 Verification / Alternative check:Difference SP1 − SP2 = 10 rupees; consistent with an additional 5% of CP = 10. Why Other Options Are Wrong:171, 180, 181: Do not equal 85% of 200. Common Pitfalls:Applying the extra 5% to the previous SP instead of to CP; confusing percentage points with compounding on SP. Final Answer:Rs. 170

Question 4

Arun buys toffees at 6 for a rupee. How many toffees per rupee should he sell to gain 20%?

Accepted Answer

Introduction:Convert the buying rate to cost per toffee, increase by 20% to get selling price per toffee, then invert to get the number per rupee. Given Data / Assumptions: Buy: 6 for Rs 1 ⇒ CP per toffee = Rs 1/6 Desired gain = 20% Concept / Approach:SP per toffee = 1.20 * (1/6) = 1/5. Then number per rupee = 1 ÷ (1/5) = 5. Step-by-Step Solution:CP per toffee = 1/6 rupeeSP per toffee = 1.2 * (1/6) = 1/5 rupeeToffees per rupee = 5 Verification / Alternative check:On 5 toffees: SP = 1 rupee. CP for 5 = 5/6 rupee. Profit = 1 − 5/6 = 1/6 rupee = 20% of 5/6 rupee. Why Other Options Are Wrong:3, 4, 6: Do not correspond to a 20% gain on the given CP.can't be determined: Sufficient information exists. Common Pitfalls:Using difference in counts directly without converting to unit prices; miscomputing 20% increase. Final Answer:5

Question 5

Mr.Mittal purchased a car for Rs. 3,00,000 and a bike for his son for Rs. 1,00,000. He sold the car at a profit of 10% and bike at a loss of 20%. What is the net gain or loss?

Accepted Answer

Gain = 10% of 3,00,000 = 30000 Loss = 20% of 1,00,000 = 20000 Net gain = 10000 over Rs.4 lakh Hence, profit = 10000/400000 x 100 = 2.5%

Question 6

A single discount equivalent to three successive discounts of 5% , 10% , 20% is :

Accepted Answer

Let the original price be 100 Rs. So reduced price = 100 X 0.95 X 0.90 X 0.80 = 68.40∴ Single discount = (100 — 68.4) % = 31.6%

Question 7

An item was sold after giving two successive discount of 20% and 10% respectively. If the item was sold for Rs. 468. The marked price of that item is :

Accepted Answer

Let the price be y , then y x 0.8 x 0.9 = 468 ∴ x=650, therefore marked price = Rs. 650Alternatively : 650 X 0.8 X 0.2 = 468 Hence option (d) is correct

Question 8

The profit percentage on the three articles A , B and C is 10%,20% and 25% and the ratio of the cost price is 1 : 2 : 4 . Also the ratio of number of articles sold of A , B and C is 2 : 5 : 2 then the overall profit percentage is :

Accepted Answer

CP of A + B + c = 2xy + 5x*2y - 2x*4y = 20xyprofit of A = 0.2xy profit of B = 2xy profit of C = 2xy Total profit = 4.2xy% profit = (4.2xy / 20xy) X 100 = 21%

Question 9

A shopkeeper sold 12 cameras at a profit of 20% and 8 cameras at a profit of 10%. If he had sold all the 20 cameras at a profit of 15% , then his profit would have been reduced by Rs. 36. what is the cost price of each camera?

Accepted Answer

Go through option C180 x 12 x 1.2 + 180 x 8 x 1.1 = 180 [ 14.4 + 8.8 ] = 180 (23.2) = 4176And 180 x 20 x 1.15 = 4140Therefore loss = 4176 - 4140 = 36 Hence option (c) is correct

Question 10

The CP of 19 articles is same as the selling price of 29 articles. what is the loss %?

Accepted Answer

CP / SP = 29x / 19x loss % = 29x - 19x / 29x X 100 = 34.48 %(To understand the concept assume CP of each article Rs 29 and SP of each article = Rs. 19)

Question 11

ITC sells one product at a profit of 20% another at a loss of 20% at the same selling price. what is the loss incurred by ITC?

Accepted Answer

Loss % = ( common gain or loss / 10 )2 % = (20 / 10)2 % = 4%

Question 12

ITC sells one product at a profit of 20% another at a loss of 20% at the same selling price. , If SP of each article be Rs. 200, what is the amount of loss?

Accepted Answer

Loss % = ( common gain or loss / 10 )2 % = (20 / 10)2 % = 4%Now assume total CP of both articles be x, then SP = 0.96x = 400 x = 400 / 0.96 = CPloss = 4% of CP = (4 / 100) X (400 / 0.96) = Rs. 16.66

Question 13

Two-stage resale chain in retail: a wholesaler sells toys to a retailer at a 20% profit on the wholesaler's cost, and the retailer then sells these toys to customers at a 25% profit on the retailer's own cost. Determine the retailer's profit percent…

Accepted Answer

Introduction:This problem separates margins at different stages in a supply chain. The retailer’s profit percentage is always calculated on the retailer’s own cost, regardless of the wholesaler’s prior profit. Given Data / Assumptions: Wholesaler → Retailer at 20% profit (affects retailer's purchase price). Retailer → Customer at 25% profit (on retailer's cost). Profit% is always with respect to the seller's own cost. Concept / Approach:Retailer's profit% = (retailer SP − retailer CP) / (retailer CP) * 100. The wholesaler’s margin only sets the retailer’s CP; it does not change the definition of the retailer’s percentage. Step-by-Step Solution:Let the retailer's cost (from wholesaler) = RRetailer sells at 25% profit ⇒ SP = R * 1.25Retailer's profit% = (1.25R − R)/R * 100 = 25% Verification / Alternative check:Try numbers: if R = 100, then SP = 125. Profit = 25, which is 25% of 100. Why Other Options Are Wrong: 5% / 20%: confuse or average margins across stages. 80%: not supported by any base change here. Common Pitfalls: Averaging 20% and 25% or compounding them on the wrong base. Final Answer:25%

Question 14

Short-supply pricing at a fuel outlet: the operator gives 5% less petrol by volume but charges at the listed cost price per litre. Compute his effective profit percentage due to short delivery.

Accepted Answer

Introduction:When quantity delivered is short but the customer pays the full tagged price per litre, the seller earns an implicit profit. The effective price per actual litre increases because less product is delivered for the same money. Given Data / Assumptions: Short delivery = 5% (customer receives 0.95 L when billed for 1 L). Charge remains at the cost price per 1 L (no visible markup). Concept / Approach:Effective price per actual litre = billed price / actual volume delivered. Profit% = (effective price − cost price)/cost price * 100. Step-by-Step Solution:Let listed cost price per litre = 1 (unit money)Actual volume delivered for 1 billed litre = 0.95 LEffective price per actual litre = 1 / 0.95 = 1.052631...Profit% = (1.052631... − 1) * 100 ≈ 5.263% ≈ 5.26% Verification / Alternative check:If cost is Rs 100 per litre billed, delivering 0.95 L means the customer effectively pays Rs 105.263 per actual litre, implying 5.263% profit over cost. Why Other Options Are Wrong: 5% / 4.78% / 5.6%: rounding or base mistakes; the exact fraction from 1/0.95 is ≈ 5.26%. Common Pitfalls: Subtracting 5% directly instead of adjusting for the new base (actual litre delivered). Final Answer:5.26%

Question 15

A buyer saves Rs 25 due to a 6.66% (i.e., 6 2/3% = 1/15) discount on a textbook. Determine the amount of money (in Rs) actually paid after discount.

Accepted Answer

Introduction:Given a discount rate and the rupee saving, you can recover the marked price and then compute the payment after discount. Given Data / Assumptions: Discount rate = 6.66% = 6 2/3% = 1/15 of the marked price (MP). Saving (discount amount) = Rs 25. Concept / Approach:Discount amount = discount_rate * MP. Amount paid = MP − discount amount. Step-by-Step Solution:Let MP = MDiscount = (1/15) * M = 25 ⇒ M = 25 * 15 = 375Amount paid = 375 − 25 = 350 Verification / Alternative check:6.66% of 375 ≈ 25; 375 − 25 = 350 confirms the payment. Why Other Options Are Wrong: 450 / 225 / 375: these are either MP or unrelated figures, not the net amount paid. Common Pitfalls: Treating 6.66% as 6% or 7% rounding, which miscomputes M. Final Answer:350

Question 16

Scooter pricing comparison: list price Rs 28,000. Dealer A offers a flat 10% discount; Dealer B offers 12% on the first Rs 20,000 and 8% on the remaining Rs 8,000. Find the difference between their selling prices.

Accepted Answer

Introduction:This question compares a single flat discount with tiered discounts. Compute each net discount in rupees, then subtract the resulting selling prices. Given Data / Assumptions: List price (LP) = Rs 28,000. Dealer A: 10% on whole LP. Dealer B: 12% on Rs 20,000 and 8% on Rs 8,000. Concept / Approach:SP = LP − (discount in rupees). Tiered discounts add linearly across their slabs. Step-by-Step Solution:Dealer A: discount = 10% of 28,000 = 2,800 ⇒ SP_A = 28,000 − 2,800 = 25,200Dealer B: discount = 12% of 20,000 (2,400) + 8% of 8,000 (640) = 3,040 ⇒ SP_B = 28,000 − 3,040 = 24,960Difference = 25,200 − 24,960 = Rs 240 Verification / Alternative check:The bigger discount is B’s by Rs 240, so his SP is lower by Rs 240, consistent with the arithmetic. Why Other Options Are Wrong: Rs 420 / Rs 640: do not match the computed slab differences. None of these: incorrect since Rs 240 is attainable. Common Pitfalls: Treating tiered percentages as a single average without computing slab-wise. Final Answer:Rs.240

Question 17

Two-article sale: one sold at 10% loss and the other at 15% profit. Overall there is no profit or loss. If the combined selling price is Rs 30,000, find the difference between their cost prices.

Accepted Answer

Introduction:When the net result is break-even, total SP equals total CP. Combine this with individual percentage relations to relate the two cost prices and then use the total SP to solve. Given Data / Assumptions: Article 1: 10% loss ⇒ SP1 = 0.9 * CP1. Article 2: 15% profit ⇒ SP2 = 1.15 * CP2. Overall: SP1 + SP2 = CP1 + CP2 and SP1 + SP2 = Rs 30,000. Concept / Approach:From break-even: 0.9CP1 + 1.15CP2 = CP1 + CP2 ⇒ 0.1CP1 = 0.15CP2 ⇒ CP1 = 1.5CP2. Then use SP total to solve CP2. Step-by-Step Solution:CP1 = 1.5 CP2Total SP = 0.9(1.5CP2) + 1.15CP2 = 1.35CP2 + 1.15CP2 = 2.5CP2 = 30,000CP2 = 12,000 ⇒ CP1 = 18,000Difference = |18,000 − 12,000| = Rs 6,000 Verification / Alternative check:SP1 = 16,200; SP2 = 13,800; sum = 30,000 equals CP1 + CP2 = 30,000, confirming break-even and the difference. Why Other Options Are Wrong: Rs 5,000 / Rs 7,500: arise from algebra mistakes in the ratio step. None of these: incorrect because Rs 6,000 is exact. Common Pitfalls: Averaging percentages or ignoring that break-even ties totals, not individual items. Final Answer:Rs.6000

Question 18

Milk adulteration and pricing: a seller buys pure milk at Rs x per litre, mixes 2 L of water with every 6 L of milk (total 8 L), and sells the mixture at Rs 2x per litre. Compute the profit percentage on cost.

Accepted Answer

Introduction:Adulteration problems require separating cost-bearing and cost-free components. Only milk costs money here; water is assumed free. Revenue is earned on the enlarged volume at the quoted selling rate. Given Data / Assumptions: Milk cost = Rs x per litre; water cost = Rs 0. Mixture: 6 L milk + 2 L water = 8 L total. Selling price of mixture = Rs 2x per litre. Concept / Approach:Total cost is from milk only. Total revenue is selling price times mixture volume. Profit% = (revenue − cost)/cost * 100. Step-by-Step Solution:Cost = 6 * x = 6xRevenue = 8 * (2x) = 16xProfit = 16x − 6x = 10xProfit% = 10x / 6x * 100 = 166.66...% (i.e., 166 2/3%) Verification / Alternative check:For x = 10, cost = 60, revenue = 160, profit = 100, which is 166.66...% of 60. Why Other Options Are Wrong: 116% / 60% / 100%: all miscompute cost components or the enlarged volume. Common Pitfalls: Including water cost or computing profit% on revenue instead of cost. Final Answer:166.66%

Question 19

An article was earlier sold at a 40% profit over cost. Later it is sold at a 20% discount on that earlier selling price. Determine the new overall profit percentage on cost.

Accepted Answer

Introduction:Successive percentage changes often apply to different bases. Here, the discount is applied to the earlier selling price, not to cost. Convert each step carefully to the correct base. Given Data / Assumptions: Original SP1 = 1.40 * C (40% profit on cost C). New SP2 = 20% discount on SP1 ⇒ SP2 = 0.80 * SP1. Concept / Approach:Chain the multipliers and then compare the final selling price with cost to get the new profit percentage. Step-by-Step Solution:SP1 = 1.40CSP2 = 0.80 * SP1 = 0.80 * 1.40C = 1.12CProfit% = (1.12C − C)/C * 100 = 12% Verification / Alternative check:Let C = Rs 100. SP1 = Rs 140. After 20% discount on 140, SP2 = Rs 112. Profit = 12 over cost = 12%. Why Other Options Are Wrong: 20% / 28% / 14%: result from applying the 20% on cost or averaging percentages incorrectly. Common Pitfalls: Applying the 20% discount to cost instead of to SP1. Final Answer:12%

Question 20

Price-tag versus transaction rates: the CP:MP ratio is 2:3. The ratio of profit percentage to discount percentage is 3:2. Assuming the same selling price links both expressions, find the discount percentage.

Accepted Answer

Introduction:Here, the selling price (SP) simultaneously equals CP increased by profit% and MP reduced by discount%. Equating these two expressions and using the given ratios yields the required discount%. Given Data / Assumptions: CP:MP = 2:3 ⇒ CP = 2k, MP = 3k. Profit% : Discount% = 3:2 ⇒ let profit% = 3t, discount% = 2t. Concept / Approach:SP = CP * (1 + profit%) = MP * (1 − discount%). Solve for t and compute discount% = 2t. Step-by-Step Solution:2k * (1 + 3t/100) = 3k * (1 − 2t/100)2 + 0.06t = 3 − 0.06t0.12t = 1 ⇒ t = 8.333... ⇒ discount% = 2t = 16.666...% Verification / Alternative check:Plugging back gives identical SP from both sides, confirming consistency. Why Other Options Are Wrong: 20% / 25% / 33.33%: stem from algebra slips or swapping bases. Common Pitfalls: Applying the 3:2 ratio to rupee profits/discounts instead of percentages. Final Answer:16.66 %

Profit and Loss Questions

Questions

Practice smarter