Question 1

Profit and Loss — Two articles are bought for ₹ 1500 and ₹ 1000. One is sold at a 20% gain. At what price should the other be sold to realize a 16% profit on the whole transaction?

Accepted Answer

Introduction / Context: To achieve an overall target profit across multiple items, compute the required total revenue, subtract what is already realized from the first sale, and the remainder is the needed selling price for the second item. Given Data / Assumptions: CP1 = ₹ 1500; CP2 = ₹ 1000; Total CP = ₹ 2500. Item 1 sold at +20% ⇒ SP1 = 1.20 * 1500 = 1800. Target overall profit = 16% on 2500 ⇒ Required total SP = 2500 * 1.16. Concept / Approach: SP_total_required = 2500 * 1.16 = 2900. Therefore, SP2_required = 2900 − SP1. This delivers the exact selling price needed for item 2 to meet the goal. Step-by-Step Solution: Total CP = 2500; Target SP_total = 2500 * 1.16 = 2900 SP1 (given) = 1800 ⇒ SP2_required = 2900 − 1800 = 1100 Thus, sell the second article at ₹ 1100 Verification / Alternative check: Profit = (1800 + 1100 − 2500) = 400 ⇒ 400/2500 * 100 = 16% (as required). Why Other Options Are Wrong: 1200, 1150, and 1250 lead to overall profits different from 16%; 1300 overshoots the target. Common Pitfalls: Applying the 16% on each item individually rather than on the combined cost; mixing up which item was sold at 20%. Final Answer: ₹ 1100

Question 2

Profit and Loss — An item sells for ₹ 60 each. It costs ₹ 40 per item to produce, and weekly fixed overheads are ₹ 3000. How many units must be produced and sold to earn at least ₹ 1000 profit per week?

Accepted Answer

Introduction / Context: This is a break-even / target-profit computation using contribution analysis. Profit equals contribution per unit times quantity minus fixed cost. Solve the inequality to meet or exceed the required profit threshold. Given Data / Assumptions: Selling price (SP) per unit = ₹ 60. Variable cost (materials + labour) = ₹ 40 per unit. Fixed overheads per week = ₹ 3000. Target profit ≥ ₹ 1000 per week. Concept / Approach: Contribution per unit = SP − VC = 20. Profit = Contribution * n − Fixed. Set Profit ≥ 1000 and solve for n. Choose the smallest integer n satisfying the inequality. Step-by-Step Solution: Contribution = 60 − 40 = 20 per unit Profit = 20n − 3000 Requirement: 20n − 3000 ≥ 1000 ⇒ 20n ≥ 4000 ⇒ n ≥ 200 Minimum feasible integer n = 200 Verification / Alternative check: At n = 200: Profit = 20*200 − 3000 = 4000 − 3000 = 1000 (meets requirement). Why Other Options Are Wrong: 150, 250, 300, 400 do not represent the minimum satisfying value; only 200 is the least n with profit ≥ 1000. Common Pitfalls: Treating fixed overhead as per-unit, or using revenue instead of contribution to compute the threshold. Final Answer: 200

Question 3

Profit and Loss — A sells an article to B at a 10% profit, and B sells it to C at a 10% loss. If C pays ₹ 2079, how much did A originally pay (A’s cost price)?

Accepted Answer

Introduction / Context: Successive percentage changes applied to the same base (the item) can be chained multiplicatively. Here, a +10% followed by −10% yields a net factor of 0.99 applied to A’s cost when reaching C’s payment amount. Given Data / Assumptions: A’s cost = x (unknown). A → B at +10% ⇒ B’s cost = 1.10x. B → C at −10% ⇒ C’s payment = 0.90 * (1.10x) = 0.99x. C pays ₹ 2079. Concept / Approach: Equate 0.99x to 2079 and solve for x. This is a straightforward reverse-percentage problem using multiplicative chaining. Step-by-Step Solution: 0.99x = 2079 ⇒ x = 2079 / 0.99 x = 2100 Therefore, A originally paid ₹ 2100 Verification / Alternative check: Forward chain: 2100 * 1.10 = 2310; 2310 * 0.90 = 2079 (matches C’s payment). Why Other Options Are Wrong: 2160 or 2400 would map through the 0.99 net factor to values different from 2079; 2480 and 2000 are arbitrary here. Common Pitfalls: Treating +10% and −10% as canceling to 0%; multiplicative chaining shows the net factor is 0.99, not 1.00. Final Answer: ₹ 2100

Question 4

Profit and Loss — A showroom sells a leather jacket at ₹ P claiming a 10% profit. At a trade fair, he marks the same jacket at ₹ 2P and allows a 20% discount. What percentage profit does he make at the trade fair (relative to his cost)?

Accepted Answer

Introduction / Context: This question compares two pricing strategies on the same cost base. First, the normal sale reveals the cost via a 10% margin. Then, the trade-fair pricing uses a 2P tag and a 20% discount, yielding a new selling price to be compared with the original cost for the revised profit percentage. Given Data / Assumptions: Normal sale: SP_normal = P at +10% ⇒ Cost (CP) = P / 1.10. Trade fair: Marked price = 2P; Discount = 20% ⇒ SP_fair = 0.80 * 2P = 1.6P. Concept / Approach: Profit factor at fair = SP_fair / CP = 1.6P / (P/1.10) = 1.6 * 1.10 = 1.76. Profit% = (1.76 − 1) * 100 = 76%. Step-by-Step Solution: CP = P / 1.10 SP_fair = 2P * 0.80 = 1.6P Profit factor = SP_fair / CP = 1.6P / (P/1.10) = 1.76 Profit% = (1.76 − 1) * 100 = 76% Verification / Alternative check: Example: If P = 110, CP = 100. Fair SP = 176 ⇒ profit = 76 on 100 ⇒ 76% (confirms). Why Other Options Are Wrong: 80% and 70% are near but incorrect; 60% understates the effect; “None of these” is unnecessary since 76% is exact. Common Pitfalls: Comparing 20% discount directly to 10% profit without adjusting bases; always compute via cost to avoid base confusion. Final Answer: 76%

Question 5

Mr. X bought a music system at a 20% discount on the labelled (marked) price. If, instead, he had received a 25% discount, he would have saved ₹500 more. At what price did he actually buy the music system (i.e., the amount he paid after 20% discount…

Accepted Answer

Introduction / Context:This discount-comparison problem asks for the actual amount paid when a 20% discount is applied. The key idea is that the difference between a 25% discount and a 20% discount equals 5% of the labelled price, which is given numerically as ₹500. Once the marked price is found, we compute the paid price at 20% off. Given Data / Assumptions: Let labelled (marked) price = M rupees. Scenario A (given): discount = 20% → paid = 0.80 * M. Scenario B (hypothetical): discount = 25% → paid = 0.75 * M. Extra saving if 25% were given instead of 20% = ₹500. Concept / Approach:The “extra saving” is exactly the difference in discounts: 25% − 20% = 5% of M. Therefore, 0.05 * M = 500, from which M is determined. Then compute the price actually paid with 20% off: 0.80 * M. Step-by-Step Solution:0.05 * M = 500M = 500 / 0.05 = ₹10,000Actual paid at 20% off = 0.80 * 10,000 = ₹8,000 Verification / Alternative check:At 25% off, paid would be 0.75 * 10,000 = ₹7,500. Difference from the 20% case = 8,000 − 7,500 = ₹500, matching the statement. Why Other Options Are Wrong:₹10,000, ₹12,000, ₹16,000: These are not the paid price after 20% discount; ₹10,000 is the marked price, not the paid price. Common Pitfalls:Mistaking the ₹500 as a discount amount at 20% rather than the difference between two discounts; reporting the marked price instead of the actual paid price. Final Answer:₹ 8,000

Question 6

A shopkeeper sold an article for ₹6,750 after giving a 10% discount on the labelled price. If he would have made a 50% profit with no discount, what was the actual percentage of profit earned with the 10% discount?

Accepted Answer

Introduction / Context:This is a labelled price and discount problem tied to a target profit without discount. We back-calculate the cost price using the hypothetical 50% profit case, and then compute the actual profit percentage when a 10% discount yields a selling price of ₹6,750. Given Data / Assumptions: Selling price with 10% discount = ₹6,750. Let labelled price = L. Then 0.90 * L = 6,750. No discount would have given 50% profit on cost. Concept / Approach:First find L from the discount relation. The no-discount scenario implies SP_no_disc = L = 1.5 * CP, so CP = L / 1.5. Then compute actual profit% = (6,750 − CP) / CP * 100. Step-by-Step Solution:L = 6,750 / 0.90 = ₹7,500CP = 7,500 / 1.5 = ₹5,000Actual profit = 6,750 − 5,000 = ₹1,750Profit% = 1,750 / 5,000 * 100 = 35% Verification / Alternative check:If sold at L (no discount), profit would be 7,500 − 5,000 = 2,500 → 50%, consistent with the premise. Why Other Options Are Wrong:36%, 40%: Do not match the computed profit over the recovered cost price. Common Pitfalls:Confusing profit on SP with profit on CP; forgetting to find CP from the “no-discount 50% profit” clue before evaluating the discounted case. Final Answer:35%

Question 7

A trader fixes the price of an article so that after giving a rebate (discount) of 10% on the fixed price, he still makes a profit of 15%. If the cost price is ₹72, what fixed (marked) price should he put on it?

Accepted Answer

Introduction / Context:This is a straightforward link between cost price, discount, and desired profit. After discounting the marked price, the resulting selling price must still deliver the target profit on cost. We equate these values to compute the required marked price. Given Data / Assumptions: Cost price (CP) = ₹72. Discount on marked price = 10%. Desired profit on CP = 15%. Concept / Approach:If M is the marked price, selling price SP = 0.90 * M. Also, target SP from cost/profit is SP = 1.15 * 72. Set these equal to find M. Step-by-Step Solution:Target SP = 1.15 * 72 = ₹82.800.90 * M = 82.80 ⇒ M = 82.80 / 0.90 = ₹92.00 Verification / Alternative check:Check: 10% off ₹92 = ₹82.80; profit = 82.80 − 72 = ₹10.80 = 15% of 72. Perfect. Why Other Options Are Wrong:₹82.80 is the selling price, not the marked price; ₹90.00 and ₹97.80 do not satisfy the exact discount-profit linkage. Common Pitfalls:Applying the 10% discount to cost instead of the marked price; mixing the profit base (CP) and discount base (M). Final Answer:₹ 92.00

Question 8

A shopkeeper wants to allow a 20% cash discount yet still earn a 20% profit on cost. What should be the marked price of an item whose cost price is ₹180?

Accepted Answer

Introduction / Context:To meet a profit target after granting a discount on the marked price, we first find the required selling price from the profit requirement, then work backward to the marked price using the discount percentage. Given Data / Assumptions: Cost price (CP) = ₹180. Desired profit = 20% on CP. Cash discount = 20% on marked price (MP). Concept / Approach:Required SP = 1.20 * CP. Also, SP = (1 − 0.20) * MP = 0.80 * MP. Equate these to solve for MP. Step-by-Step Solution:Required SP = 1.20 * 180 = ₹2160.80 * MP = 216 ⇒ MP = 216 / 0.80 = ₹270 Verification / Alternative check:Applying 20% off on ₹270 gives ₹216; profit over ₹180 is ₹36 → 20%. Why Other Options Are Wrong:₹240, ₹245, ₹260: After 20% off, these do not yield a selling price of ₹216. Common Pitfalls:Adding discounts and profits directly; using CP as the discount base by mistake rather than the marked price. Final Answer:₹ 270

Question 9

A trader allows a discount of 10% on the marked price. By what percentage above the cost price should the article be marked so that the trader still makes a 17% profit?

Accepted Answer

Introduction / Context:We must connect the desired profit to the ultimate selling price after discount. The marked price must be set high enough so that a 10% discount still leaves a 17% margin on cost. Given Data / Assumptions: Let cost price (CP) = C rupees. Desired profit = 17% on C ⇒ target SP = 1.17 * C. Discount on marked price (MP) = 10% ⇒ SP = 0.90 * MP. Concept / Approach:Equate the two expressions for SP to compute MP relative to C, then convert to the percentage markup required over C. Step-by-Step Solution:0.90 * MP = 1.17 * CMP = (1.17 / 0.90) * C = 1.30 * CThus, markup over cost = 30%. Verification / Alternative check:If C = 100, choose MP = 130; discount 10% → SP = 117; profit = 17 which is 17% of 100. Why Other Options Are Wrong:25%, 28%, 24%: Do not reconcile with SP = 117% of CP after a 10% reduction on MP. Common Pitfalls:Subtracting 10 from 17 directly; applying percentages on the wrong base (CP vs MP). Final Answer:30%

Question 10

Ravi bought a scooter at 11/13 of its marked price and sold it at 10% more than the marked price. What was his gain percentage on cost?

Accepted Answer

Introduction / Context:This problem mixes a purchase below marked price and a sale above marked price. We treat the marked price as a bridge variable to express both the cost price and the selling price, and then compute profit% on cost. Given Data / Assumptions: Let marked price = M. Cost price (CP) = (11/13) * M. Selling price (SP) = 1.10 * M. Concept / Approach:Profit% = (SP − CP) / CP * 100. Substituting CP and SP in terms of M allows M to cancel out, leaving a pure percentage. Step-by-Step Solution:Profit = 1.10M − (11/13)M = M * (1.10 − 0.8461538...) = (33/130)MProfit% = [(33/130)M] / [(11/13)M] * 100 = (33/130) * (13/11) * 100 = 30% Verification / Alternative check:Pick M = 130 for simplicity: CP = 110; SP = 143; profit = 33; profit% = 33/110 * 100 = 30%. Why Other Options Are Wrong:24%, 27%, 32%: Do not match the exact ratio obtained from the given fractions. Common Pitfalls:Calculating profit% on SP; arithmetic slips with fractions or decimal conversion. Final Answer:30%

Question 11

A dealer buys an article marked ₹40,000 with successive discounts of 20% and 10%. He spends ₹1,200 on repairs and then sells it for ₹30,000. What is his overall result (gain or loss percentage)?

Accepted Answer

Introduction / Context:Successive discounts multiply, not add. After applying both discounts to the marked price, we add repair costs to determine the effective cost. Comparing the final selling price with this effective cost yields the net result. Given Data / Assumptions: Marked price = ₹40,000. Discounts: 20% then 10% (successive). Repairs = ₹1,200. Selling price = ₹30,000. Concept / Approach:Effective purchase price = 40,000 * 0.80 * 0.90. Total cost = effective purchase price + repairs. Compare with SP for gain/loss%: (SP − total cost) / total cost * 100. Step-by-Step Solution:Purchase price = 40,000 * 0.80 * 0.90 = 40,000 * 0.72 = ₹28,800Total cost = 28,800 + 1,200 = ₹30,000Net result = SP − total cost = 30,000 − 30,000 = 0 → no gain, no loss Verification / Alternative check:Discount equivalence: 20% and then 10% equals 28% overall only if mis-added; the correct multiplicative approach gives 28.8% off, matching ₹28,800. Why Other Options Are Wrong:10% gain or loss do not align with the exact parity between total cost and SP. Common Pitfalls:Adding discounts linearly; forgetting to include repair costs when computing the effective base cost. Final Answer:No gain no loss

Question 12

A dishonest dealer claims to sell at cost price but uses a false weight of 900 g as “1 kg”. What is his gain percentage on the true cost of goods delivered?

Accepted Answer

Introduction / Context:Short-weight frauds create profit even when the dealer “sells at cost price.” The trick is that the customer is charged for 1 kg but actually receives less. We compare revenue for the billed 1 kg with the true cost of the quantity actually delivered. Given Data / Assumptions: Dealer bills 1 kg at cost price per kg = C rupees. Actual quantity delivered = 0.9 kg (900 g). Cost base for profit% is the cost of goods delivered. Concept / Approach:Revenue per “1 kg” bill = C. Cost of delivered goods = 0.9 * C. Profit = C − 0.9C = 0.1C. Profit% on cost = (0.1C)/(0.9C) * 100 = 11.111...%. Step-by-Step Solution:Revenue = CCost (0.9 kg) = 0.9CProfit = 0.1CProfit% = (0.1/0.9) * 100 = 11.111...% = 11 1/9 % Verification / Alternative check:On 9 kg actually supplied (billed as 10 kg), total billed amount = 10C; cost = 9C; profit = C; profit% = C/9C = 11.11%. Why Other Options Are Wrong:10% and 11% are approximations that underestimate; 12 1/2% is too high. Common Pitfalls:Computing profit% on selling price; forgetting that the base should be cost of quantity actually delivered. Final Answer:11 1/9 %

Question 13

A shopkeeper sells wheat at a quoted profit of 10% and also uses weights that are 20% short (he delivers only 0.8 kg when billing 1 kg). What is his total gain percentage on true cost?

Accepted Answer

Introduction / Context:This combines an explicit price margin with a short-weight trick. The overall profit is computed relative to the cost of the actual quantity delivered, not the billed quantity. Given Data / Assumptions: True cost per kg = C. Quoted price profit = 10% ⇒ billed price per 1 “kg” = 1.10 * C. Delivered quantity per billed kg = 0.8 kg. Concept / Approach:For one billed kilogram: revenue = 1.10C; cost of delivered goods = 0.8C. Profit% on cost = (revenue − cost)/cost * 100 = (1.10C − 0.8C)/(0.8C) * 100. Step-by-Step Solution:Profit = 0.30CCost base = 0.80CProfit% = 0.30C / 0.80C * 100 = 37.5% Verification / Alternative check:On 4 kg actually delivered (billed as 5 kg), revenue = 5 * 1.10C = 5.5C; cost = 4C; profit = 1.5C; profit% = 1.5/4 * 100 = 37.5%. Why Other Options Are Wrong:30% ignores short-weight; 88% is far too high; “None” is invalid. Common Pitfalls:Using selling price as the profit base; overlooking that short-weight increases effective price per true kg. Final Answer:37.5%

Question 14

By selling an umbrella at price P there is a profit of x%. If selling at two-thirds of that price (2/3 P) results in a 10% loss, what is the profit percentage at price P?

Accepted Answer

Introduction / Context:We relate the selling price to cost using the loss information at a fractional price. Once we express P in terms of cost, the profit% at P follows directly. Given Data / Assumptions: If sold at (2/3)P, loss = 10% ⇒ (2/3)P = 0.90 * C. We need profit% at price P. Concept / Approach:From (2/3)P = 0.90C, solve for P in terms of C, then compute profit% = (P − C)/C * 100. Step-by-Step Solution:(2/3)P = 0.90C ⇒ P = 0.90 * (3/2) * C = 1.35CProfit at P = (1.35C − C)/C * 100 = 35% Verification / Alternative check:Check the loss case: at 0.666...P = 0.9C indeed corresponds to 10% below cost, as used. Why Other Options Are Wrong:25% or 30% do not match the linear relationship between P and C implied by the (2/3)P loss condition. Common Pitfalls:Misplacing the 2/3 factor or applying the 10% to SP instead of CP. Final Answer:35%

Question 15

Charu purchased a dinner set and later sold it at 10% above her cost price. (Recovery-first clarification: interpret “purchased at 3/10 of its selling price” as a redundant/erroneous fragment). What was her gain percentage?

Accepted Answer

Introduction / Context:The original stem reads “purchased at 3/10th of its selling price and sold it at 10% more than its CP,” which is self-contradictory if “selling price” refers to the actual final selling price. Applying the Recovery-First Policy, we retain the computable and standard portion: she sold the item at 10% more than cost price. We then answer for gain percentage based on that corrected, solvable interpretation. Given Data / Assumptions: Recovered assumption: selling price (SP) = 1.10 * cost price (CP). No other reliable numeric data is needed for gain%. Concept / Approach:Profit% on cost is computed as (SP − CP)/CP * 100. With SP = 1.10 * CP, the profit% follows immediately. Step-by-Step Solution:SP = 1.10 * CPProfit% = (1.10CP − CP)/CP * 100 = 10% Verification / Alternative check:For CP = 100 (representative): SP = 110; profit = 10; profit% = 10/100 * 100 = 10%. Why Other Options Are Wrong:15%, 5%, 9%: Do not match the direct 10% uplift over cost. Common Pitfalls:Taking the ambiguous phrase “3/10th of its selling price” at face value with the final SP, which would contradict the stated 10% uplift. Final Answer:10%

Question 16

A furniture shop owner charges 18% above cost price. If a customer paid ₹10,207 for a dining table, find the original cost price.

Accepted Answer

Introduction / Context:Selling price being a fixed percentage above cost enables direct back-calculation. We simply divide the paid amount by 1.18 to recover the cost price (CP). Given Data / Assumptions: Selling price (SP) = ₹10,207. SP = 1.18 * CP. Concept / Approach:Rearrange to CP = SP / 1.18. This is a classic reverse-percentage calculation. Step-by-Step Solution:CP = 10,207 / 1.18 = ₹8,650 Verification / Alternative check:Check: 8,650 * 1.18 = 8,650 + 1,557 = ₹10,207, confirming the exact match to the paid amount. Why Other Options Are Wrong:₹9,240/₹9,840/₹7,670 do not yield ₹10,207 upon multiplying by 1.18. Common Pitfalls:Subtracting 18% of SP rather than dividing by 1.18; mixing discount logic with markup logic. Final Answer:₹ 8650

Question 17

Meena purchased two fans at ₹1,200 each. She sold one at a 5% loss and the other at a 10% gain. What is her overall percentage result (gain or loss) on the combined transaction?

Accepted Answer

Introduction / Context:When two items have equal costs but unequal gain/loss percentages, total result is found by summing individual selling prices and comparing to total cost. Here, both items cost ₹1,200, simplifying aggregation. Given Data / Assumptions: Fan A: CP = ₹1,200, sold at 5% loss ⇒ SP_A = 0.95 * 1,200 = ₹1,140. Fan B: CP = ₹1,200, sold at 10% gain ⇒ SP_B = 1.10 * 1,200 = ₹1,320. Total CP = ₹2,400. Concept / Approach:Total SP = SP_A + SP_B, then compute overall profit% = (Total SP − Total CP)/Total CP * 100. Step-by-Step Solution:Total SP = 1,140 + 1,320 = ₹2,460Overall profit = 2,460 − 2,400 = ₹60Overall profit% = 60 / 2,400 * 100 = 2.5% Verification / Alternative check:Since costs are equal, the average of the percentage gains/losses weighted by cost roughly indicates direction; here positive net because +10% outweighs −5% over equal bases. Why Other Options Are Wrong:1.2% profit/loss and 2.5% loss contradict the exact aggregation results. Common Pitfalls:Averaging 10% and −5% as 2.5% directly works only because costs are equal; otherwise, weighted averages are needed. Final Answer:2.5% profit

Question 18

A woman bought eggs at ₹30 per dozen. What should be the selling price per 100 eggs to gain 12%?

Accepted Answer

Introduction / Context:Convert the purchase rate per dozen into a cost per egg, scale to 100 eggs, and then apply the desired 12% profit to obtain the required selling price per hundred eggs. Given Data / Assumptions: Cost per dozen = ₹30 → cost per egg = 30/12 = ₹2.50. We need SP for 100 eggs with 12% profit. Concept / Approach:Total cost for 100 eggs = 100 * 2.50. Selling price = cost * 1.12. Simple percentage gain on cost. Step-by-Step Solution:Cost for 100 eggs = 100 * 2.50 = ₹250Required SP = 250 * 1.12 = ₹280 Verification / Alternative check:Profit = 280 − 250 = ₹30 which is 12% of ₹250, confirming correctness. Why Other Options Are Wrong:₹250 is cost; ₹300 and ₹360 overshoot the 12% target. Common Pitfalls:Forgetting that a dozen is 12; applying 12% to the wrong base. Final Answer:280

Question 19

A man buys an equal number of oranges at two rates: 4 a rupee and 5 a rupee. He mixes them and sells the mixture at 4 a rupee. What is his overall percentage result (gain or loss)?

Accepted Answer

Introduction / Context:This is a mixture pricing problem with equal counts. Compute total cost from the two purchase rates, then the selling revenue at a single mixed rate, and finally compare for gain or loss percentage on total cost. Given Data / Assumptions: Let n be the number bought at each rate. Cost1 per orange = ₹0.25 (4 a rupee); Cost2 per orange = ₹0.20 (5 a rupee). Selling price per orange = ₹0.25 (4 a rupee). Concept / Approach:Total cost = n(0.25) + n(0.20) = 0.45n. Total oranges = 2n. Total revenue at 0.25 each = 0.50n. Profit% = (Revenue − Cost)/Cost * 100. Step-by-Step Solution:Total cost = 0.45nTotal revenue = 0.50nProfit = 0.05nProfit% = (0.05n) / (0.45n) * 100 = 11.111...% = 11 1/9 % gain Verification / Alternative check:Choose n = 20. Cost = 9; revenue = 10; profit = 1; profit% = 1/9 * 100 = 11.11%. Why Other Options Are Wrong:Loss options are invalid since revenue exceeds cost; 12 1/2% is higher than the exact fraction 1/9. Common Pitfalls:Using an average of rates instead of computing exact totals; forgetting counts are equal (not costs). Final Answer:11 1/9 % gain

Question 20

Selling an article at a certain price yields a 10% profit. If instead the article is sold at double that price, what is the new profit percentage?

Accepted Answer

Introduction / Context:We relate selling prices to cost via the initial 10% profit. Doubling the selling price doubles revenue, not cost, so the profit percentage changes nonlinearly with respect to cost. Given Data / Assumptions: If selling at price P gives 10% profit, then P = 1.10 * C, where C is cost price. New selling price = 2P. Concept / Approach:Compute 2P relative to C and then determine profit% = (SP − C)/C * 100. Step-by-Step Solution:P = 1.10C ⇒ 2P = 2.20CNew profit = 2.20C − C = 1.20CProfit% = 1.20C / C * 100 = 120% Verification / Alternative check:Take C = 100. Then P = 110; doubling gives 220; profit = 120 → 120% of cost. Why Other Options Are Wrong:20%/40% are far too small; “100” lacks percent and is numerically wrong. Common Pitfalls:Doubling profit percentage instead of recomputing from cost; forgetting initial 10% defines P relative to C. Final Answer:120%

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