Question 1

Changing cost and price together: A man sells an article at a profit of 40%. If instead he had bought it at 40% less (than the original cost) and sold it for ₹ 5 less than his original selling price, he would have gained 50%. Find the original cost …

Accepted Answer

Introduction / Context: This problem links two scenarios through the same original selling price (minus ₹ 5) and a changed cost. Setting up an equation between the alternative selling price and the required 50% gain on the reduced cost yields the original CP. Given Data / Assumptions: Original SP = 1.40 * C (40% profit on original cost C). Alternative cost = 0.60 * C (40% less). Alternative SP = (original SP) − ₹ 5, and at this price the gain would be 50% on the reduced cost. Concept / Approach: Equation: (1.40C − 5) = 1.50 * (0.60C) = 0.90C. Solve for C. Step-by-Step Solution: 1.40C − 5 = 0.90C0.50C = 5C = ₹ 10 Verification / Alternative check: Original SP = 1.40 * 10 = ₹ 14. Alternative SP = 14 − 5 = ₹ 9. Reduced cost = 0.60 * 10 = ₹ 6. Profit at ₹ 9 is ₹ 3, which is 50% of ₹ 6—verified. Why Other Options Are Wrong: ₹ 15 / ₹ 20 / ₹ 30: do not satisfy the equation 1.40C − 5 = 0.90C. Common Pitfalls: Applying 50% to the original cost instead of to the reduced cost. Final Answer: ₹ 10

Question 2

Profit percentage numerically equal to cost price: A person sells a watch for ₹ 75 and the percentage profit equals the cost price (in rupees). Find the cost price of the watch.

Accepted Answer

Introduction / Context: Some puzzles equate a numerical percentage to a rupee value. Here, the profit percentage number equals the cost price itself, leading to a quadratic relation between SP and CP. Given Data / Assumptions: SP = ₹ 75. Let CP = x. Profit% = x (numerically). Concept / Approach: Profit% = (SP − CP)/CP * 100. Setting this equal to x gives: (75 − x)/x * 100 = x ⇒ 75 − x = x^2/100 ⇒ x^2 + 100x − 7,500 = 0. Step-by-Step Solution: Solve x^2 + 100x − 7,500 = 0Discriminant = 100^2 + 4*7,500 = 40,000 ⇒ √D = 200x = (−100 + 200)/2 = 50 (reject negative root) Verification / Alternative check: If CP = ₹ 50, profit = ₹ 25. Profit% = 25/50 * 100 = 50, which equals the CP numerically—condition satisfied. Why Other Options Are Wrong: ₹ 40 / ₹ 45 / ₹ 55: do not satisfy the quadratic relation with SP = 75. Common Pitfalls: Treating “profit% equals CP” as profit equals CP; the statement is about the numeric percent equaling the rupee CP. Final Answer: ₹ 50

Question 3

Mixing equal quantities at different costs: Two lots of onions of equal weight are mixed—one costing ₹ 10 per kg and the other ₹ 15 per kg. The entire mixture is sold at ₹ 15 per kg. Compute the percentage profit or loss.

Accepted Answer

Introduction / Context: When equal quantities are mixed, the average cost per kg is the simple average of the two rates. Compare the selling price per kg to this average cost to determine profit%. Given Data / Assumptions: Equal-weight lots at ₹ 10/kg and ₹ 15/kg. Mixture sold at ₹ 15/kg. Concept / Approach: Average cost per kg = (10 + 15)/2 = ₹ 12.50. Profit% = (SP − AvgCost)/AvgCost * 100. Step-by-Step Solution: Average cost = ₹ 12.50 per kgSelling price = ₹ 15 per kgProfit per kg = 15 − 12.50 = ₹ 2.50Profit% = 2.50 / 12.50 * 100 = 20% Verification / Alternative check: Take 1 kg from each lot (total 2 kg). Total cost = 10 + 15 = ₹ 25. Revenue = 2 * 15 = ₹ 30. Profit = ₹ 5 = 20% of ₹ 25—confirms the calculation. Why Other Options Are Wrong: 10% profit: too low; average cost is ₹ 12.50 not ₹ 13.50. 10% loss / 20% loss: sign is incorrect since SP exceeds average cost. Common Pitfalls: Using a weighted average other than 50:50; the problem states equal quantities. Final Answer: 20% profit

Question 4

Unit pricing with gain → recover buying rate per dozen A vendor sells lemons at a rate of 5 for ₹14 and earns a 40% profit on this selling rate. At what total price did he buy 1 dozen (12) lemons?

Accepted Answer

Introduction / Context: This is a classic profit-and-loss unit-rate question. We are told the seller makes a 40% profit when selling lemons at a quoted “x for ₹y” rate. From the selling rate (per lemon) and the gain percentage, we can reverse-calculate the true cost per lemon and then scale to a dozen. Given Data / Assumptions: Selling rate: 5 lemons for ₹14. Profit rate on cost: 40%. Find: total cost for 12 lemons (1 dozen). Assume identical quality and uniform cost per lemon. Concept / Approach: Compute the selling price per lemon, then divide by (1 + gain%) to get the cost price per lemon. Finally multiply the per-lemon cost by 12 to get the cost of a dozen. Step-by-Step Solution: SP per lemon = 14 / 5 = ₹2.80.Gain% = 40% ⇒ SP = 1.40 * CP ⇒ CP per lemon = 2.80 / 1.40 = ₹2.00.Cost for 12 lemons = 12 * 2.00 = ₹24. Verification / Alternative check: If CP per lemon is ₹2, then for 5 lemons CP = ₹10, SP = ₹14, profit = ₹4, which is 40% of ₹10. This confirms the backward calculation. Why Other Options Are Wrong: ₹20 underestimates because it treats the profit as lower than 40%.₹21 and ₹26 do not align with 2.80 / 1.40 = 2.00 per lemon.₹28 corresponds to a higher per-lemon cost than allowed by a 40% margin at the given SP. Common Pitfalls: Applying 40% to the selling price instead of the cost price, or scaling the “5 for ₹14” rate directly to a dozen without removing the profit first. Final Answer: ₹ 24

Question 5

Reverse a loss scenario to a gain target — oranges count for a fixed sum By selling 32 oranges for ₹30, a man incurs a 25% loss. How many oranges should he sell for ₹24 to make a 20% gain instead?

Accepted Answer

Introduction / Context: This question connects two different profit scenarios with fixed-sum selling: first a loss at a known pack-rate, then a desired gain at a new total price. The key is to recover the true cost per orange from the loss case, then set a selling rate to reach the target gain for the new money amount. Given Data / Assumptions: Loss case: 32 oranges sold for ₹30 with 25% loss. Target case: Sell for ₹24 with 20% gain. Uniform cost per orange; quality unchanged. Concept / Approach: From the first case, compute SP per orange, then divide by 0.75 to get CP per orange (since a 25% loss means SP = 0.75 * CP). For the target case, SP per orange must be 1.20 * CP. With total SP fixed at ₹24, the count follows by division. Step-by-Step Solution: SP per orange (loss case) = 30 / 32 = ₹0.9375.CP per orange = 0.9375 / 0.75 = ₹1.25.Required SP per orange for 20% gain = 1.20 * 1.25 = ₹1.50.For ₹24 total: number of oranges n = 24 / 1.50 = 16. Verification / Alternative check: If 16 are sold for ₹24, SP per orange is ₹1.50; profit per orange is ₹0.25 on cost ₹1.25, which is exactly 20% gain. Why Other Options Are Wrong: 24, 28, or 32 would result in SP per orange lower than ₹1.50, missing the 20% gain.20 would overshoot the required margin. Common Pitfalls: Using 25% and 20% on selling price instead of cost, or scaling counts without first finding the true unit cost. Final Answer: 16

Question 6

Landed cost with freight, octroi, and handling → target 40% margin Kamlesh purchases 120 reams of paper at ₹100 per ream, pays ₹480 transport, octroi at ₹0.50 per ream, and ₹60 in coolie charges. At what selling price per ream should he sell to gain…

Accepted Answer

Introduction / Context: Landed cost aggregates all acquisition expenses before pricing for profit: item price, transport, statutory duties, and handling. Once the total landed cost is known, apply the target margin to obtain the total revenue and divide by total units to get the per-unit selling price. Given Data / Assumptions: Basic purchase: 120 * ₹100 = ₹12,000. Transport: ₹480. Octroi: ₹0.50 per ream * 120 = ₹60. Coolie/handling: ₹60. Target gain: 40% on total cost. Concept / Approach: Total landed cost = sum of all cost components. Target revenue = landed cost * 1.40. Selling price per ream = Target revenue / 120. Step-by-Step Solution: Landed cost = 12,000 + 480 + 60 + 60 = ₹12,600.Target revenue = 12,600 * 1.40 = ₹17,640.SP per ream = 17,640 / 120 = ₹147. Verification / Alternative check: Per-ream landed cost = 12,600 / 120 = ₹105. A 40% markup gives 105 * 1.40 = ₹147, confirming the result. Why Other Options Are Wrong: ₹138 and ₹150 do not correspond to a 40% margin on the computed landed cost.₹155 and ₹165 overshoot the required profit percentage. Common Pitfalls: Ignoring small per-unit duties like octroi, or applying 40% to the basic purchase cost instead of the full landed cost. Final Answer: ₹ 147

Question 7

Mixture pricing — blend two teas and compute gain on selling price A tea producer blends two varieties: ₹18 per kg and ₹20 per kg in the ratio 5:3 by weight. If the blended tea is sold at ₹21 per kg, what is the gain percentage on cost?

Accepted Answer

Introduction / Context: Mixture problems in profit-and-loss require finding the weighted-average cost price of the blend and then comparing it with the selling price to obtain the margin on cost. Given Data / Assumptions: Component prices: ₹18/kg and ₹20/kg. Mixing ratio: 5 : 3 by weight. Selling price of blended tea: ₹21/kg. Concept / Approach: Average cost price = (5*18 + 3*20) / (5 + 3). Gain% = (SP − CP_avg) / CP_avg * 100. Step-by-Step Solution: Average CP = (90 + 60)/8 = 150/8 = ₹18.75 per kg.Profit per kg = 21 − 18.75 = ₹2.25.Gain% = 2.25 / 18.75 * 100 = 12%. Verification / Alternative check: If 8 kg are blended: total cost = 5*18 + 3*20 = ₹150; revenue at ₹21/kg for 8 kg = ₹168; profit = ₹18 which is 12% of ₹150. Why Other Options Are Wrong: 8%, 10%, 15%, and 18% do not match the exact ratio-weighted average leading to ₹18.75 cost. Common Pitfalls: Using a simple (18+20)/2 average without ratio weighting, or computing profit% on SP instead of CP. Final Answer: 12%

Question 8

Pens bought and sold in packs — compute true gain percentage Pens are bought at 5 for ₹4 (purchase pack rate) and sold at 4 for ₹5 (selling pack rate). What is the gain percentage?

Accepted Answer

Introduction / Context: When items are priced as “x for ₹y”, always convert to per-unit cost and per-unit selling price. The profit percentage is then computed on the cost price per unit, not the selling price. Given Data / Assumptions: Buy 5 pens for ₹4 ⇒ CP per pen. Sell 4 pens for ₹5 ⇒ SP per pen. Find gain% on cost. Concept / Approach: CP per pen = 4/5. SP per pen = 5/4. Gain% = (SP − CP)/CP * 100. Step-by-Step Solution: CP per pen = ₹4/5 = ₹0.80.SP per pen = ₹5/4 = ₹1.25.Gain per pen = 1.25 − 0.80 = ₹0.45.Gain% = 0.45 / 0.80 * 100 = 56.25%. Verification / Alternative check: On 20 pens: cost = 4 packs of 5 → ₹16; sell as 5 packs of 4 → ₹25; profit = ₹9 on ₹16 = 56.25% (same result). Why Other Options Are Wrong: 55% and 52% are close but not exact; 45.26% and 60% deviate further from the correct calculation. Common Pitfalls: Mixing the bases (computing percentage on SP), or averaging the pack rates instead of converting to per-unit prices first. Final Answer: 56.25%

Question 9

Pack-rate twist — buy 11 for ₹10, sell 10 for ₹11 A person buys 11 identical articles for ₹10 and sells them at a rate of 10 articles for ₹11. What is his gain percentage?

Accepted Answer

Introduction / Context: This is another “x for ₹y” conversion problem. Converting both purchase and selling packs to per-unit prices allows a straightforward profit percentage calculation on cost. Given Data / Assumptions: Buy 11 for ₹10 ⇒ CP per unit. Sell 10 for ₹11 ⇒ SP per unit. Uniform quality, identical articles. Concept / Approach: Compute CP per unit and SP per unit, then calculate gain% = (SP − CP)/CP * 100. Step-by-Step Solution: CP per article = 10/11.SP per article = 11/10.Gain% = ((11/10 − 10/11) / (10/11)) * 100.Compute: (121 − 100)/110 * 11/10 * 100 = (21/110) * (11/10) * 100 = 21%. Verification / Alternative check: Numerical check: CP ≈ ₹0.9091, SP = ₹1.10, margin ≈ ₹0.1909; 0.1909 / 0.9091 ≈ 0.21 = 21%. Why Other Options Are Wrong: 20% and 22% are near but not exact; 19% and 1% are incorrect by larger margins. Common Pitfalls: Forgetting that profit percentage is on CP, not on SP, and attempting to average the pack rates directly. Final Answer: 21%

Question 10

Profit equals the selling price of some units — infer overall gain By selling 100 pens, a shopkeeper’s profit equals the selling price of 40 pens. What is his gain percentage on the entire lot?

Accepted Answer

Introduction / Context: If a seller’s profit (in rupees) equals the selling price of a certain number of units, we can represent totals algebraically and cancel unknowns cleanly. This type of question emphasizes understanding the relationship between total selling price, total cost price, and profit. Given Data / Assumptions: Total items sold: 100 pens. Profit amount = SP of 40 pens. Uniform unit price for all pens in the transaction. Concept / Approach: Let s be the SP per pen. Then total SP = 100s and profit = 40s. Hence total cost = total SP − profit = 60s. Profit% = profit / cost * 100 = (40s)/(60s) * 100. Step-by-Step Solution: Let SP per pen = s; Total SP = 100s.Profit = 40s.Total cost = 100s − 40s = 60s.Gain% = (40s / 60s) * 100 = 66.666...% = 66.67%. Verification / Alternative check: Assume s = ₹1 for simplicity. Then total SP = ₹100, profit = ₹40, cost = ₹60, which indeed gives a 40/60 = 2/3 = 66.67% gain. Why Other Options Are Wrong: 6.67%, 8.8%, 5.59%, and 44.7% misinterpret the profit relation or the base used for the percentage. Common Pitfalls: Taking percentage on SP rather than on CP, or assuming profit equals the cost of 40 pens (the statement says selling price of 40 pens). Final Answer: 66.67%

Question 11

When CP of 16 equals SP of 12 — identify profit percentage If the cost price of 16 pens equals the selling price of 12 pens (same kind), what is the profit percentage?

Accepted Answer

Introduction / Context: Comparing total cost for some units with total selling price for a different number of the same units reveals the SP-to-CP ratio per item. From this ratio we can read off the profit or loss percentage directly. Given Data / Assumptions: Total CP of 16 items equals total SP of 12 items. All items identical; uniform per-unit CP and SP. Concept / Approach: Let CP per pen be C and SP per pen be S. Then 16C = 12S ⇒ S/C = 16/12 = 4/3. Since S > C, there is a profit. Profit% = (S − C)/C * 100 = (4/3 − 1) * 100 = 1/3 * 100. Step-by-Step Solution: From 16C = 12S, S/C = 4/3 ≈ 1.3333.Profit fraction = (4/3 − 1) = 1/3.Profit% = (1/3) * 100 = 33 1/3% gain. Verification / Alternative check: Assume C = ₹3 per pen ⇒ 16C = ₹48. Then S = 4/3 * 3 = ₹4 per pen; 12 pens at ₹4 gives ₹48, consistent. Profit per pen = ₹1 on ₹3 ⇒ 33 1/3%. Why Other Options Are Wrong: 25% gain/loss and 33 1/3% loss contradict S/C = 4/3 > 1. Common Pitfalls: Inverting the ratio to 3/4 by mistake or labeling the outcome as loss instead of profit. Final Answer: 33 1/3% gain

Question 12

False weights with nominal loss — dealer uses 20% less weight A dishonest dealer sells at a quoted 10% loss on cost price but secretly delivers only 80% of the claimed weight. What is his true profit or loss percentage?

Accepted Answer

Introduction / Context: When sellers use short weights, the effective quantity delivered is lower than claimed. Even if a price suggests a loss relative to cost for the full weight, the reduced quantity delivered can flip the outcome to a real profit. We compare revenue per “claimed kg” with the actual cost of the lesser quantity handed over. Given Data / Assumptions: Quoted loss on cost: 10% (i.e., SP for 1 kg = 0.90 * CP per kg). Actual delivered weight for 1 kg claimed = 0.80 kg. Uniform cost per kg. Concept / Approach: Let CP per kg = 100 units. Then SP per claimed kg = 90. Actual cost for delivered 0.80 kg = 0.80 * 100 = 80. True gain% = (Revenue − Actual cost)/Actual cost * 100. Step-by-Step Solution: Assume CP per kg = 100.Quoted SP for “1 kg” = 90 (10% loss reference).Actual weight delivered = 0.80 kg ⇒ cost incurred = 80.True profit = 90 − 80 = 10 ⇒ Profit% = 10/80 * 100 = 12.5% gain. Verification / Alternative check: Equivalent formula: True factor = (SP factor)/(weight factor) relative to CP; here 0.90/0.80 = 1.125 ⇒ 12.5% gain. Matches the detailed computation. Why Other Options Are Wrong: 22.5% and 10% gain misapply either the loss or weight factor; the loss options contradict the net > 1 factor of 1.125. Common Pitfalls: Applying the 10% to the delivered weight instead of the price, or forgetting to compute profit relative to actual cost (not claimed 1 kg). Final Answer: 12.5% gain

Question 13

Marked profit plus short weight — combined effect on gain A trader sells wheat at a marked 20% profit but uses a weight that is 20% less than the true measure (delivers only 0.8 kg for each 1 kg claimed). What is his overall gain percentage?

Accepted Answer

Introduction / Context: Short-weight malpractice amplifies profit beyond the price markup. We combine the price factor with the weight factor to get the true gain relative to cost. Given Data / Assumptions: Price markup: +20% on CP ⇒ price factor = 1.20. Delivered weight factor: 0.80 of claimed. Uniform CP per true kg. Concept / Approach: Let CP per true kg = 100. Revenue per claimed kg at +20% = 120. Actual cost for 0.80 kg delivered = 0.80 * 100 = 80. True gain% = (120 − 80) / 80 * 100. Step-by-Step Solution: Revenue per claimed kg = 120.Actual cost incurred = 80.Profit = 40 ⇒ Profit% = 40/80 * 100 = 50%. Verification / Alternative check: Combined factor view: effective multiplier on cost = 1.20 / 0.80 = 1.50 ⇒ 50% gain. Same result. Why Other Options Are Wrong: 35%, 38%, and 48% underestimate the combined effect; 60% overshoots. Common Pitfalls: Adding percentages arithmetically instead of using multiplicative factors, or forgetting the weight reduction effect. Final Answer: 50%

Question 14

Quoted loss with 30% short weight — find the true outcome A dishonest dealer sells at a quoted 10% loss on cost but delivers only 70% of the correct weight. What is his true profit or loss percentage?

Accepted Answer

Introduction / Context: Short weight can turn an apparent loss into a real profit. We compare the revenue per claimed unit (using the quoted price) against the actual cost of the smaller quantity delivered to find the true percentage outcome on cost. Given Data / Assumptions: Quoted price implies 10% loss on CP for 1 kg ⇒ SP per claimed kg = 0.90 * CP per kg. Only 70% of the weight is delivered per claimed kg. Uniform CP per true kg. Concept / Approach: Let CP per true kg = 100. Then revenue per claimed kg = 90. Actual cost incurred (0.70 kg) = 70. True profit% = (Revenue − Cost)/Cost * 100. Step-by-Step Solution: Assume CP per kg = 100 ⇒ SP per claimed kg = 90.Actual cost for 0.70 kg = 70.Profit = 90 − 70 = 20.Profit% = 20 / 70 * 100 = 28.571...% = 28 4/7% gain. Verification / Alternative check: Factor method: effective multiplier = 0.90 / 0.70 = 1.285714... ⇒ 28 4/7% gain, confirming the result. Why Other Options Are Wrong: Loss options contradict factor > 1; 28 3/7% and 16 3/7% do not match 0.90/0.70 exactly; 'no profit, no loss' is not supported. Common Pitfalls: Computing percentage on SP instead of cost, or subtracting percentages linearly instead of using the ratio approach. Final Answer: 28 4/7% gain

Question 15

Claims to sell at cost but uses 920 g as “1 kg” — find true gain A dealer professes to sell at cost price but uses a 920 g weight instead of 1 kg. What is his gain percentage?

Accepted Answer

Introduction / Context: Short-weight tricks produce profit even when the posted price equals cost price. Charging for 1 kg while delivering only 920 g yields a gain because the seller's cost is incurred on a smaller mass than billed. Given Data / Assumptions: Charge as if 1 kg is delivered, at cost price per kg. Actual delivered mass = 0.92 kg. Uniform cost per true kg. Concept / Approach: If CP per true kg = C, then revenue for a “1 kg” sale = C. Actual cost incurred = 0.92C. Profit fraction on cost = (C − 0.92C)/(0.92C) = (0.08/0.92) = 8/92 = 2/23. Convert to percent for the answer. Step-by-Step Solution: Profit fraction = 1/0.92 − 1 = (1 − 0.92)/0.92 = 0.08/0.92 = 2/23.Profit% = (2/23) * 100 = 200/23 % = 8 16/23%. Verification / Alternative check: Numerical check: Take C = ₹100: charge ₹100 but incur cost on 0.92 kg = ₹92; profit = ₹8; profit% = 8/92 * 100 ≈ 8.6956% = 8 16/23%. Why Other Options Are Wrong: Other percentages do not equal 200/23% and therefore do not match a 920 g short weight. Common Pitfalls: Using 8% directly instead of 8/92, or confusing percent of SP with percent of CP. Final Answer: 8 16/23% gain

Question 16

Quoted 4% loss but uses 28 g in place of 32 g — true outcome A dealer claims a 4% loss on price but gives only 28 g instead of 32 g per dose. What is his actual profit or loss percentage?

Accepted Answer

Introduction / Context: In short-weight scenarios, actual cost is for less quantity than billed. Even with a quoted loss, the reduced quantity can turn the outcome into a net gain. We translate the 28 g versus 32 g situation into cost-revenue comparisons for one “claimed dose.” Given Data / Assumptions: Quoted loss on price: 4% → SP per claimed 32 g = 0.96 * CP for 32 g. Actual delivered mass per dose = 28 g. Uniform cost per gram. Concept / Approach: Let cost per gram = c. Then CP for 32 g = 32c; quoted SP = 0.96 * 32c = 30.72c. Actual cost incurred = 28c. Profit% = (30.72c − 28c) / (28c) * 100. Step-by-Step Solution: Profit = 30.72c − 28c = 2.72c.Profit% = 2.72c / 28c * 100 = (2.72/28) * 100.2.72/28 = 0.097142857... ⇒ Profit% ≈ 9.7142857% = 68/7% gain. Verification / Alternative check: Factor form: effective multiplier = 0.96 / (28/32) = 0.96 / 0.875 = 1.097142857... ⇒ 9.7142857% gain, identical to 68/7%. Why Other Options Are Wrong: Loss options contradict factor > 1; 16 3/7% and 14 3/7% do not match the 0.96 / 0.875 ratio; 9% underestimates the exact value. Common Pitfalls: Applying 4% to the delivered 28 g incorrectly, or computing percentage on SP rather than on cost. Final Answer: 68/7% gain

Question 17

When CP of 20 equals SP of 15 — compute profit percentage If the cost price of 20 articles equals the selling price of 15 articles (same type), find the profit percentage.

Accepted Answer

Introduction / Context: Total cost equaling total revenue for different counts reveals the SP/CP ratio per unit. This directly gives profit percentage without needing explicit rupee values. Given Data / Assumptions: 20 * CP per unit = 15 * SP per unit. Identical items with uniform unit prices. Concept / Approach: From 20C = 15S ⇒ S/C = 20/15 = 4/3. Profit% = (S − C)/C * 100 = (4/3 − 1)*100 = 1/3*100. Step-by-Step Solution: S/C = 4/3.Profit fraction = 1/3.Profit% = 33 1/3 %. Verification / Alternative check: Let C = ₹3 ⇒ S = ₹4. Then 20C = ₹60 and 15S = ₹60 (consistent). Profit per unit = ₹1 on ₹3 ⇒ 33 1/3%. Why Other Options Are Wrong: 33 1/2%, 33 1/5%, 33 1/7% and 25% do not match the exact 4/3 ratio. Common Pitfalls: Inverting the ratio to 3/4 or claiming loss instead of profit. Final Answer: 33 1/3 %

Question 18

Equal selling price on two items: +20% on one, −20% on the other A furniture seller sells two tables for ₹1500 each. He gains 20% on one table and loses 20% on the other. What is the net result over the two sales?

Accepted Answer

Introduction / Context: Equal selling prices do not imply equal percentage outcomes, because the cost bases differ. Compute the cost for each table from its SP and percentage, then compare total SP and total CP to determine the overall result. Given Data / Assumptions: Table A: SP = ₹1500 with 20% gain. Table B: SP = ₹1500 with 20% loss. Concept / Approach: From SP = CP * (1 ± 0.20), recover each CP. Sum CPs and SPs and compute percentage change: (Total SP − Total CP)/Total CP * 100. Step-by-Step Solution: CP_A = 1500 / 1.20 = ₹1250.CP_B = 1500 / 0.80 = ₹1875.Total CP = 1250 + 1875 = ₹3125; Total SP = 1500 + 1500 = ₹3000.Net = 3000 − 3125 = −₹125 ⇒ Loss% = 125/3125 * 100 = 4% loss. Verification / Alternative check: Relative reasoning: +20% and −20% around different bases cannot cancel; the larger base (loss item) dominates, producing a net loss. Why Other Options Are Wrong: 4% profit and 'neither' ignore the base effect; 10% or 2% loss do not match the precise arithmetic. Common Pitfalls: Assuming +20% and −20% cancel arithmetically; percentage changes must be applied multiplicatively to their respective bases. Final Answer: 4% loss

Question 19

Switch from 6% loss to 6% gain changes SP by ₹6 — find CP If an article, when sold at a 6% loss, instead were sold at a 6% gain, the seller would get ₹6 more. What is the cost price?

Accepted Answer

Introduction / Context: A symmetric switch from −6% to +6% around cost implies a total swing of 12% of the cost price in the selling price. The given rupee change immediately reveals the cost when divided by 0.12. Given Data / Assumptions: Difference between SPs at −6% and +6% = ₹6. Both percentages are on the same CP base. Concept / Approach: Change = (6% + 6%) of CP = 12% of CP. So CP = Change / 0.12. Step-by-Step Solution: 0.12 * CP = 6 ⇒ CP = 6 / 0.12 = ₹50. Verification / Alternative check: At CP = ₹50: SP at −6% = 47; SP at +6% = 53; difference = ₹6, matching the condition. Why Other Options Are Wrong: ₹94, ₹100, ₹106, and ₹60 do not satisfy 12% of CP = 6. Common Pitfalls: Applying 12% to SP instead of CP, or halving the difference by mistake. Final Answer: ₹ 50

Question 20

Two equal selling prices: one house at +20%, the other at −20% A man sells two houses for ₹96,000 each. On the first he makes a 20% profit; on the second he incurs a 20% loss. What is the overall percentage result?

Accepted Answer

Introduction / Context: Equal selling prices with opposite percentages do not cancel because the cost bases differ. We compute cost for each, sum, and compare with the total selling amount to get the net percentage. Given Data / Assumptions: Both SPs = ₹96,000. First: +20% profit; Second: −20% loss. Concept / Approach: CP_1 = 96,000 / 1.20; CP_2 = 96,000 / 0.80. Net = (SP_1 + SP_2) − (CP_1 + CP_2). Percentage = Net / (CP_1 + CP_2) * 100. Step-by-Step Solution: CP_1 = ₹80,000; CP_2 = ₹120,000.Total CP = ₹200,000; Total SP = ₹192,000.Net = 192,000 − 200,000 = −₹8,000 ⇒ Loss% = 8,000/200,000 * 100 = 4% loss. Verification / Alternative check: Relative base logic: the loss operates on the larger base (₹120,000) and outweighs the gain on the smaller base (₹80,000), producing a net loss. Why Other Options Are Wrong: 6% or 4% gain contradict the numeric totals; 'no profit, no loss' ignores base dependence; 6% loss is too large. Common Pitfalls: Adding +20 and −20 as if they cancel; percentages are multiplicative and base-dependent. Final Answer: 4% loss

Profit and Loss Questions