Question 1

A trader sells sugar at Rs 400 for 20 kg (i.e., Rs 20 per kg). A customer negotiates 20% price discount, but the trader short-weighs by 4% per kg delivered. What is the customer’s effective discount percentage versus the original list price per actu…

Accepted Answer

Introduction:When both price and quantity change, compute the effective price per actual kilogram delivered. Short weight reduces the benefit of the price discount. Given Data / Assumptions: Original price = Rs 20 per kg. Discounted billed price = 20% off ⇒ Rs 16 per billed kg. Short weight = 4% ⇒ actual delivery per billed kg = 0.96 kg. Concept / Approach:Effective price per actual kg = billed price / actual quantity delivered. Effective discount% compares this with the original Rs 20 per actual kg. Step-by-Step Solution:Effective price per actual kg = 16 / 0.96 = 16.666...Effective discount% = (20 − 16.666...)/20 * 100 = 16.666...% Verification / Alternative check:If the customer pays Rs 16 for 0.96 kg, scaling to 1 kg costs 16.666..., which is 1/6 less than 20, i.e., 16 2/3%. Why Other Options Are Wrong: 16% / 15.5% / 19.6%: each miscomputes the base or mixes up the order of changes. Common Pitfalls: Applying the 4% to the price instead of to the weight delivered. Final Answer:16.66 %

Question 2

Fuel adulteration: a trader mixes “25% kerosene to petrol” and sells the mixture at the price of petrol. If kerosene costs 50% of petrol, find the net profit percentage (assume “25% to petrol” means kerosene equals 25% of petrol volume; i.e., 1 part…

Accepted Answer

Introduction:Ambiguous phrasing “mixes 25% kerosene to petrol” is commonly interpreted as adding kerosene equal to 25% of the petrol volume (not that the final mixture is 25% kerosene). Under that standard reading, kerosene becomes 1/5 of the final mixture. Given Data / Assumptions: Let petrol price = P per litre; kerosene price = 0.5P per litre. Mixing rule: for 4 L petrol add 1 L kerosene ⇒ total 5 L mixture (20% kerosene). Mixture sold at price of petrol = P per litre. Concept / Approach:Compute cost per litre of the mixture from component costs, then compare to SP per litre (which equals P). Profit% = (SP − CP)/CP * 100. Step-by-Step Solution:Component cost for 5 L: 4L*P + 1L*0.5P = 4P + 0.5P = 4.5PCost per litre of mixture = 4.5P / 5 = 0.9PSP per litre = P ⇒ Profit per litre = P − 0.9P = 0.1PProfit% = 0.1P / 0.9P * 100 = 11.111...% = 11 1/9 % Verification / Alternative check:If instead the statement meant 25% of the final mixture is kerosene, profit would be 14 2/7%, which does not match the given options. Hence we adopt the standard interpretation producing 11 1/9 %. Why Other Options Are Wrong: 12 1/9 % / 9 1/11 % / 20 %: not aligned with the cost-per-litre calculation under the stated assumption. Common Pitfalls: Misreading “25% to petrol” as “25% of the mixture,” changing the ratio and answer. Final Answer:11 1/9 %

Question 3

A trader buys from a wholesaler whose balance reads 1200 g for what is truly 1000 g (over-reading scale). The trader then marks up goods by 20% above his cost and sells to customers (use a correct scale). Determine the trader’s overall profit or los…

Accepted Answer

Introduction:Faulty weights affect the actual quantity received for a given billed weight. If a wholesaler’s scale over-reads, the buyer receives less than billed. We must combine this effect with the retailer’s 20% markup to find the net outcome. Given Data / Assumptions: Wholesaler’s reading 1200 g corresponds to true 1000 g (over-reading by factor 1.2). Retailer pays per “kg” by reading, but actually receives only 5/6 kg true per billed kg. Retailer uses a correct scale for selling and marks up 20% on his cost per kg. Concept / Approach:Per billed kg at cost C, true quantity received = 5/6 kg. If the retailer sets selling price at 20% above cost per kg, revenue per true kg = 1.2C. Multiply by true kg received to compare total revenue with total cost. Step-by-Step Solution:Cost for 1 billed kg = C; true quantity received = 5/6 kgRetailer’s SP per true kg = 1.2C (20% markup on cost)Revenue from that batch = (5/6) * 1.2C = CThus revenue equals cost ⇒ 0% net profit/loss Verification / Alternative check:Scaling the batch size or cost leaves the product (5/6 * 1.2) unchanged at 1.00, so the conclusion is robust. Why Other Options Are Wrong: 38% / 50% profit: ignore the short-quantity factor canceling the 20% markup. None of the above: incorrect because 0% is exact. Common Pitfalls: Assuming both wholesaler and retailer use faulty balances, which is not stated. Final Answer:no profit no loss

Question 4

A trader sells 100 articles and earns a profit equal to the selling price of 75 articles. Compute his profit percentage on cost.

Accepted Answer

Introduction:When profit is expressed as a multiple of selling price of some quantity, convert it into algebra with per-unit selling price to find cost and then the profit percentage. Given Data / Assumptions: Let s be the selling price per article. Total articles sold = 100. Profit amount = selling price of 75 articles = 75s. Concept / Approach:Total SP = 100s. Cost = SP − Profit. Profit% = Profit / Cost * 100. Step-by-Step Solution:Total SP = 100sProfit = 75sTotal Cost = 100s − 75s = 25sProfit% = 75s / 25s * 100 = 300% Verification / Alternative check:Numbers: if s = 1, SP = 100, profit = 75, cost = 25 ⇒ 75/25 * 100 = 300%. Why Other Options Are Wrong: 33.33% / 75% / 150%: each uses the wrong base (SP) or misreads the condition. Common Pitfalls: Calculating profit% on selling price rather than on cost price. Final Answer:300%

Question 5

Profit & loss — linked prices for tables and chairs The cost of 2 tables equals the cost of 5 chairs. The difference between the price of one table and one chair is Rs 1200. Find the cost of one chair.

Accepted Answer

Introduction / Context:In profit and loss and basic algebra questions, proportional price relations are common. Here, the prices of tables and chairs are related by a ratio, and a fixed difference is also given. We must use simultaneous relations to compute the unit price of a chair. Given Data / Assumptions: 2 tables cost = 5 chairs cost. Difference between the price of 1 table and 1 chair = Rs 1200. All items are identical in type and quality. Concept / Approach:Translate the statements into algebra using unit prices: let T be the cost of one table and C be the cost of one chair. From 2T = 5C, we get T = 2.5C. Use the given difference T - C to form a second equation and solve for C. Step-by-Step Solution:Let T = price of one table, C = price of one chair.Given: 2T = 5C ⇒ T = 2.5C.Difference: T - C = 1200.Substitute T = 2.5C: 2.5C - C = 1200 ⇒ 1.5C = 1200.Therefore, C = 1200 / 1.5 = 800. Verification / Alternative check:If C = 800, then T = 2.5 × 800 = 2000. Difference T - C = 2000 - 800 = 1200 (matches). Also 2T = 4000 and 5C = 4000 (consistent). Why Other Options Are Wrong:Rs 600, Rs 700, Rs 900, Rs 1,000 do not satisfy both equations simultaneously. Common Pitfalls:Confusing the ratio 2T = 5C as T:C = 2:5 (it is actually T:C = 2.5:1). Forgetting to use the difference equation leads to underdetermination. Final Answer:Rs 800

Question 6

Unit-rate conversion — quarter kilogram to grams If 1/4 kg costs Rs 0.60, what is the price for 200 g?

Accepted Answer

Introduction / Context:This question tests proportional reasoning when converting between kilograms and grams. Once the per-gram cost is determined (or scaled proportionally), we can compute the price for 200 g directly. Given Data / Assumptions: Cost of 1/4 kg (250 g) = Rs 0.60. Find the cost for 200 g. Price varies linearly with weight (uniform unit price). Concept / Approach:Use direct proportion: cost is proportional to weight. Either compute per-gram price or scale 200 g as a fraction of 250 g. Step-by-Step Solution:250 g costs 60 paise.200 g is (200/250) = 0.8 of 250 g.So cost for 200 g = 0.8 × 60 paise = 48 paise. Verification / Alternative check:Per-gram price = 60/250 = 0.24 paise per gram. For 200 g: 200 × 0.24 = 48 paise (confirms). Why Other Options Are Wrong:40 or 45 paise underestimate; 50 or 60 paise overestimate relative to proportional scaling. Common Pitfalls:Mixing rupees and paise or confusing 1/4 kg with 200 g. Note 1/4 kg = 250 g, not 200 g. Final Answer:48 paise

Question 7

Bulk-cost estimation — bananas price scaling If 1/4 dozen bananas cost Rs 2.35, estimate the total cost of 42 dozen bananas (approximate).

Accepted Answer

Introduction / Context:This is an approximation problem using proportional scaling from a known small batch price (quarter dozen) to a large batch (dozens). You must convert between units consistently and round sensibly. Given Data / Assumptions: 1/4 dozen = 3 bananas cost Rs 2.35. We need the approximate cost for 42 dozen bananas. Assume constant unit price per banana. Concept / Approach:Find the per-banana price, compute the number of bananas in 42 dozen, multiply, and round to a nearby option. Approximation is acceptable as asked. Step-by-Step Solution:1/4 dozen = 3 bananas → per banana price = 2.35 / 3 ≈ 0.7833.42 dozen = 42 × 12 = 504 bananas.Total cost ≈ 504 × 0.7833 ≈ 395.0.Approximate to nearest option: ≈ Rs 400. Verification / Alternative check:Scale in two steps: 1 dozen = 4 × (1/4 dozen) ⇒ 1 dozen ≈ 4 × 2.35 = 9.40. For 42 dozen: 42 × 9.40 = 394.8 ≈ 395 (same conclusion). Why Other Options Are Wrong:Rs 430 and Rs 460 are too high; Rs 380 is low; Rs 540 is far from proportional scaling. Common Pitfalls:Confusing 1/4 dozen with 1 banana, or forgetting 1 dozen = 12 pieces. Also, not rounding correctly to the nearest plausible option. Final Answer:Rs 400

Question 8

Brick consignment costing — include carriage 7000 bricks cost Rs 5740 and carriage (luggage) to site costs Rs 805. What is the total cost per thousand bricks?

Accepted Answer

Introduction / Context:In materials costing (common in civil works or procurement), you must include both purchase price and carriage to compute the effective rate per thousand units. This problem asks for a combined unit rate. Given Data / Assumptions: Cost of 7000 bricks = Rs 5740. Carriage (luggage) = Rs 805. Find cost per 1000 bricks including carriage. Concept / Approach:Add the two cost components, then divide by the number of thousand-brick lots in 7000. Finally, compute the per-thousand rate. Step-by-Step Solution:Total effective cost = 5740 + 805 = 6545.Quantity = 7000 bricks = 7 thousands.Rate per thousand = 6545 / 7 = 935. Verification / Alternative check:Unit cost per brick = 6545 / 7000 ≈ 0.935; multiply by 1000 ⇒ 935 (consistent). Why Other Options Are Wrong:800 and 750 ignore carriage or mis-divide; 900 and 970 do not match total/quantity arithmetic. Common Pitfalls:Forgetting to add carriage or dividing by 1000 rather than the number of thousand-brick groups (7). Final Answer:Rs 935

Question 9

Rate scaling — mangoes bulk estimation If 357 mangoes cost Rs 1517.25, approximate the total price for 49 dozen mangoes.

Accepted Answer

Introduction / Context:Bulk price estimation questions require converting quantities and applying a constant unit rate. Here, we estimate the price for dozens given a total cost for a different count. Given Data / Assumptions: 357 mangoes cost Rs 1517.25. Need cost for 49 dozen = 49 × 12 = 588 mangoes. Assume uniform price per mango. Concept / Approach:Find price per mango, then scale up to 588 mangoes, and round to the nearest available option as it is an approximate calculation. Step-by-Step Solution:Per mango cost = 1517.25 / 357 = 4.25 exactly (since 357 × 4.25 = 1517.25).Quantity needed = 49 dozen = 588 mangoes.Total cost = 588 × 4.25 = 2499.0 ≈ Rs 2500. Verification / Alternative check:Compute 4.25 × 600 = 2550; subtract 4.25 × 12 = 51; gives 2499 (same approximation). Why Other Options Are Wrong:Rs 2600 and Rs 3000 are too high; Rs 2200 is too low; Rs 2700 also overshoots. Common Pitfalls:Incorrect dozen conversion (1 dozen = 12) or rounding prematurely before multiplying by 588 can distort the result. Final Answer:Rs 2500

Question 10

Finding gain percent from selling price and profit amount An article is sold for Rs 100 with a gain of Rs 10. What is the gain percentage?

Accepted Answer

Introduction / Context:Gain percent is computed on cost price, not on selling price. When you know the selling price and the absolute profit, first derive the cost price, then compute the percentage gain relative to cost. Given Data / Assumptions: Selling price (SP) = Rs 100. Profit (gain) = Rs 10. Find gain % on cost price (CP). Concept / Approach:Profit = SP - CP. Gain % = (Profit / CP) * 100. Use the given numbers to find CP and then the percentage. Step-by-Step Solution:Profit = 10, SP = 100 ⇒ CP = SP - Profit = 100 - 10 = 90.Gain % = (10 / 90) * 100 = 11.111... %.As a mixed fraction, 11 1/9%. Verification / Alternative check:If CP = 90 and gain is 11 1/9%, then SP = 90 × (1 + 1/9) = 90 × (10/9) = 100 (matches data). Why Other Options Are Wrong:9% and 10% use the wrong base; 12 1/2% overshoots. 'None of these' is incorrect because 11 1/9% is exact. Common Pitfalls:Computing gain % on SP instead of CP, or rounding 11.11% to 10% incorrectly. Final Answer:11 1/9%

Question 11

Reverse percent — recover cost price from selling price By selling an article for Rs 247.50, the profit is 12 1/2%. What is the cost price?

Accepted Answer

Introduction / Context:When the selling price and profit percent are known, cost price is obtained by dividing SP by (1 + profit%). Here, 12 1/2% = 1/8 = 0.125. Given Data / Assumptions: SP = Rs 247.50. Profit % = 12 1/2% = 0.125. Concept / Approach:SP = CP × (1 + profit%). Therefore, CP = SP / (1 + profit%). Step-by-Step Solution:1 + profit% = 1 + 0.125 = 1.125.CP = 247.50 / 1.125 = 220. Verification / Alternative check:Check forward: CP = 220; profit = 12.5% of 220 = 27.5; SP = 220 + 27.5 = 247.5 (matches). Why Other Options Are Wrong:210, 224, 225, 230 do not satisfy SP = CP × 1.125 exactly. Common Pitfalls:Using 12.5% as 0.12 or rounding 1.125, which leads to small errors. Final Answer:Rs 220

Question 12

Loss percent from CP–SP relation across counts If the cost of 15 tables equals the selling price of 20 identical tables, what is the loss percentage?

Accepted Answer

Introduction / Context:This question compares total cost and total selling price for different counts of the same item. The ratio of SP to CP per unit reveals profit or loss percentage. Given Data / Assumptions: 15 × CP = 20 × SP for identical tables. Find loss % (if any). Concept / Approach:From 15C = 20S ⇒ S/C = 15/20 = 3/4. Since S < C, there is a loss. Loss % = (C - S)/C × 100 = (1 - S/C) × 100. Step-by-Step Solution:S/C = 3/4 = 0.75.Loss % = (1 - 0.75) × 100 = 25%. Verification / Alternative check:Assume CP = 100 ⇒ SP = 75 (from ratio). Loss = 25 on 100 ⇒ 25% (matches). Why Other Options Are Wrong:20% and 30% are off; 37.5% would correspond to S/C = 0.625, which is not implied. Common Pitfalls:Inverting the ratio or assuming profit instead of loss. Always check whether SP is less than CP. Final Answer:25%

Question 13

Equal profit–loss from two selling prices Selling at Rs 425 gives the same profit as the loss when selling at Rs 355. What is the cost price?

Accepted Answer

Introduction / Context:When profit from one selling price equals loss from another, the cost price lies exactly midway between those selling prices. We can also show this algebraically. Given Data / Assumptions: Profit at SP1 = Rs 425 equals loss at SP2 = Rs 355. Find cost price (CP). Concept / Approach:If 425 - CP = CP - 355, then CP is the average of 425 and 355. Solve directly or via averages. Step-by-Step Solution:Set 425 - CP = CP - 355.2 × CP = 425 + 355 = 780.CP = 780 / 2 = 390. Verification / Alternative check:Profit at 425: 425 - 390 = 35. Loss at 355: 390 - 355 = 35. Equal as given. Why Other Options Are Wrong:385 or 395 breaks the equality; 400 and 405 give unequal profit and loss. Common Pitfalls:Adding instead of averaging, or mixing up which side is profit or loss. Final Answer:Rs 390

Question 14

Finding loss percent from SP and absolute loss An article is sold for Rs 100 incurring a loss of Rs 10. What is the loss percentage?

Accepted Answer

Introduction / Context:Loss percent is always calculated on cost price. When selling price and absolute loss are known, first compute the cost price, then use loss% = (loss / CP) * 100. Given Data / Assumptions: SP = Rs 100. Loss = Rs 10. Find loss % on CP. Concept / Approach:Loss = CP - SP, so CP = SP + Loss. Then compute percentage relative to CP. Step-by-Step Solution:CP = 100 + 10 = 110.Loss % = (10 / 110) * 100 = 9.0909... % = 9 1/11%. Verification / Alternative check:If CP = 110 and loss is 9 1/11% (= 1/11), then loss = 110 × (1/11) = 10 and SP = 100 (matches data). Why Other Options Are Wrong:10% uses SP as base; 8 1/3% and 11 1/9% do not match the computed CP. Common Pitfalls:Computing the percentage on SP instead of CP or rounding 9.09% improperly to 10%. Final Answer:9 1/11%

Question 15

Buy–sell comparison on count and unit price A man buys 10 articles for Rs 8 and sells each for Rs 1.25. What is his gain percentage?

Accepted Answer

Introduction / Context:Here we compare per-unit cost and per-unit selling price. Converting the bulk purchase into a unit cost is the first step, followed by computing gain% on cost price. Given Data / Assumptions: 10 articles cost Rs 8 ⇒ CP per article = Rs 0.80. SP per article = Rs 1.25. Concept / Approach:Gain per article = SP - CP. Gain % = (Gain / CP) * 100. Step-by-Step Solution:CP per article = 8 / 10 = 0.80.Gain per article = 1.25 - 0.80 = 0.45.Gain % = (0.45 / 0.80) * 100 = 56.25% = 56 1/4%. Verification / Alternative check:On 10 items: total CP = 8, total SP = 12.5, total gain = 4.5; gain% = (4.5/8)*100 = 56.25% (same). Why Other Options Are Wrong:20% and 50% underestimate; 37 1/2% is incorrect; 62 1/2% overestimates the gain. Common Pitfalls:Using SP as the base for percentage or misreading '10 for Rs 8' as '8 for Rs 10'. Final Answer:56 1/4%

Question 16

Recovering cost price from selling price and profit percent A radio is sold for Rs 1980 at a gain of 10%. What was its cost price?

Accepted Answer

Introduction / Context:Given SP and profit %, cost price is found by dividing by (1 + profit%). This is a standard reverse-percentage operation in profit and loss. Given Data / Assumptions: SP = Rs 1980. Profit % = 10% = 0.10. Concept / Approach:SP = CP × (1 + profit%). Therefore, CP = SP / 1.10. Step-by-Step Solution:CP = 1980 / 1.10 = 1800. Verification / Alternative check:10% of 1800 = 180; SP = 1800 + 180 = 1980 (confirms). Why Other Options Are Wrong:1782 is 10% off 1980 (wrong base); 2178 is higher than SP; 1650 and 1880 fail the 10% forward check. Common Pitfalls:Taking 10% of SP rather than CP when reversing, or dividing by 0.10 instead of 1.10. Final Answer:Rs 1800

Question 17

Relating CP and SP percentages What percent of the selling price equals 34% of the cost price if gross profit is 26% of the selling price?

Accepted Answer

Introduction / Context:We are asked to express a fraction of cost price as a percentage of selling price, given a profit relation to selling price. This requires expressing CP in terms of SP and then scaling the specified fraction. Given Data / Assumptions: Gross profit = 26% of SP ⇒ SP - CP = 0.26 SP. Hence CP = 0.74 SP. We need 34% of CP as a percent of SP. Concept / Approach:Compute 34% of CP and then divide by SP to convert it to a percentage of SP. Step-by-Step Solution:CP = 0.74 SP.34% of CP = 0.34 × 0.74 SP = 0.2516 SP.Therefore, as a percent of SP: 0.2516 × 100 = 25.16. Verification / Alternative check:Using fractions: CP/SP = 74/100, then 34% of CP = (34/100) × (74/100) SP = 2516/10000 SP = 25.16% of SP. Why Other Options Are Wrong:17.16 and 26.84 arise from mixing bases; 74.00 and 88.40 are unrelated to the computed chain. Common Pitfalls:Accidentally using profit% on CP or applying 34% directly to SP rather than CP. Final Answer:25.16

Question 18

Mixture average price and total gain Alok mixes 25 kg at Rs 6/kg with 35 kg at Rs 7/kg and sells the 60 kg mixture at Rs 6.75/kg. What is the overall gain or loss?

Accepted Answer

Introduction / Context:When mixing two lots sold as a single mixture, compute the weighted-average cost price and compare with the selling price. Multiply the per-kg margin by total kg to get total gain or loss. Given Data / Assumptions: Lot 1: 25 kg at Rs 6/kg. Lot 2: 35 kg at Rs 7/kg. Mixture sold at Rs 6.75/kg; total quantity = 60 kg. Concept / Approach:Average CP = (Total cost) / (Total kg). Gain per kg = SP - Avg CP. Total gain = gain per kg × total kg. Step-by-Step Solution:Total cost = 25 × 6 + 35 × 7 = 150 + 245 = 395.Average CP = 395 / 60 ≈ 6.5833.SP = 6.75 ⇒ Gain per kg ≈ 0.1667.Total gain ≈ 0.1667 × 60 = 10. Verification / Alternative check:Direct difference method confirms: (SP − CP_avg) × 60 = (6.75 − 395/60) × 60 = 10. Why Other Options Are Wrong:Rs 16 gain/loss and Rs 20 gain do not follow from the computed average and margin. Common Pitfalls:Using simple average of prices ( (6 + 7)/2 ) instead of weighted average by quantities. Final Answer:Rs 10.00 gain

Question 19

Unit conversion and target profit count A buys oranges at Rs 2 for 3 oranges and sells at Rs 1 per orange. How many oranges must be sold to make a profit of Rs 10?

Accepted Answer

Introduction / Context:This problem converts a 'bulk price' to a per-unit cost and compares it with a per-unit selling price to find the required quantity for a target profit. Given Data / Assumptions: CP: Rs 2 for 3 oranges ⇒ CP per orange = 2/3. SP per orange = Rs 1. Target profit = Rs 10. Concept / Approach:Profit per orange = SP − CP. Number of oranges needed = Target profit / Profit per orange. Step-by-Step Solution:CP per orange = 2/3 ≈ 0.6667.Profit per orange = 1 − 2/3 = 1/3 ≈ 0.3333.Required count = 10 / (1/3) = 30 oranges. Verification / Alternative check:Total revenue for 30 oranges = 30 × 1 = 30; total cost = 30 × 2/3 = 20; profit = 10 (matches target). Why Other Options Are Wrong:20 or 24 underachieve the target; 36 or 40 exceed the minimum needed. Common Pitfalls:Misreading 'Rs 2 for 3' as 'Rs 3 for 2' or computing profit percent instead of count. Final Answer:30 oranges

Question 20

Solving two-item linear price equations The cost of 2 T.V. sets and 1 radio is Rs 7000, while the cost of 2 radios and 1 T.V. set is Rs 4250. Find the cost of one T.V. set.

Accepted Answer

Introduction / Context:This is a simple system of linear equations with two unknowns (prices of a T.V. set and a radio). Solving simultaneously yields the unit prices. Given Data / Assumptions: 2T + R = 7000. T + 2R = 4250. Find T. Concept / Approach:Use elimination: scale one equation to align coefficients and subtract to find one variable, then back-substitute. Step-by-Step Solution:(1) 2T + R = 7000.(2) T + 2R = 4250.Double (2): 2T + 4R = 8500.Subtract (1): 3R = 1500 ⇒ R = 500.Substitute in (2): T + 2×500 = 4250 ⇒ T = 3250. Verification / Alternative check:Check (1): 2×3250 + 500 = 7000 (holds). Check (2): 3250 + 2×500 = 4250 (holds). Why Other Options Are Wrong:3000, 3160, 3240 are not solutions to the system; 'None of these' is inapplicable since 3250 is exact. Common Pitfalls:Arithmetic slips when eliminating, or mixing the equations when substituting back. Final Answer:Rs 3250

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