Practice Questions
Concept Explanation
Mixed problems combine CP, SP, MP, discount, false weight, and overall profit. Strategy:
- Write the full chain from CP to final SP.
- Convert each step to a multiplier on CP.
- Solve for the unknown and check whether profit% is on CP or SP.
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Q1 EasyGoods costing Rs. 750 are marked up by 20% and then sold at a 20% discount on the marked price. The final selling price is:ExplanationSP = 750 × 1.20 × 0.80 = Rs. 720.
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Q2 MediumIf a man buys 1 litre of milk for Rs. 12 and mixes it with 20% water and sells it for Rs. 15, then the profit is:Explanation1.2 L mixture at CP Rs. 12 gives CP/litre = Rs. 10. Profit = Rs. 5 per litre = 50% on CP.
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Q3 MediumA vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to get 20% profit?ExplanationCP per toffee = 1/6. SP for 20% profit = 1/5 rupee per toffee → 5 for a rupee.
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Q4 MediumA reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for Rs. 240. The original price per kg of sugar was:Explanation240/P − 240/(0.8P) = 6 → P = Rs. 10 per kg.
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Q5 MediumIf the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is:Explanation12 CP = 8 SP → SP = 1.5 CP → gain = 50%.
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Q6 MediumAn article costing Rs. 720 is marked 25% above cost price and sold after a 10% discount on the marked price. The profit on the article is:ExplanationMP = Rs. 900. SP = 900 × 0.90 = Rs. 810. Profit = 810 − 720 = Rs. 90.
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Q7 MediumAn article with marked price Rs. 1,100 is sold after a 10% discount. If the cost price is Rs. 800, the profit percentage on cost price is:ExplanationSP = 1100 × 0.90 = Rs. 990. Profit = Rs. 190. Profit% = 190/800 × 100 = 23.75% ≈ 24%.
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Q8 MediumTwo articles costing Rs. 600 and Rs. 400 are sold at 20% profit and 10% loss respectively. The overall profit percentage on the total cost price of Rs. 1,000 is:ExplanationTotal SP = 720 + 360 = Rs. 1,080. Net profit Rs. 80 → 8% on total CP.
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Q9 MediumAn article costing Rs. 900 must be sold at 10% profit after allowing a 10% discount on the marked price. The required marked price is:ExplanationRequired SP = Rs. 990. MP = 990/0.90 = Rs. 1,100.
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Q10 HardA shopkeeper sold an article offering a discount of 5% and earned a profit of 31.25%. What would have been the percentage of profit earned if no discount had been offered?ExplanationSP = 1.3125 CP and 0.95 MP = SP → MP = 1.38158 CP. Profit without discount = 38.125% on CP.
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Q11 HardA man bought an article and sold it at a gain of 5%. If he had bought it at 5% less and sold it for Rs. 2 less, he would have gained 10%. The cost price of the article is:ExplanationLet CP = x. 1.05x − 2 = 1.10(0.95x) → x = Rs. 400.
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Q12 HardA trader marks his goods 50% above cost price and allows two successive discounts of 10% each on the marked price. The net profit percentage on cost price is:ExplanationSP = 1.5 × 0.9 × 0.9 = 1.215 CP → 21.5% profit on CP.
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Q13 HardA shopkeeper marks an article 30% above cost price, allows 20% discount on the marked price, and uses a weight of 900 g instead of 1 kg while selling at the quoted price. The approximate total gain percentage is:ExplanationPrice multiplier = 1.3 × 0.8 = 1.04. False-weight gain = (1000 − 900)/900 ≈ 11.1%. Combined ≈ 1.04 × 1.111 − 1 ≈ 15.6% total gain.
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Q14 HardAn article costing Rs. 400 is sold at 10% profit. If the cost price had been 10% lower with the same selling price, the profit percentage on the new cost price would have been:ExplanationSP = Rs. 440. New CP = Rs. 360. Profit% = 80/360 × 100 ≈ 22.2%.
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DS1 Medium
A sales coordinator needs the final selling price after an advertised markdown on a newly listed product. What is the selling price?
Statement IThe cost price of the product is Rs. 800.
Statement IIThe marked price is 25% above cost price and a 10% discount is allowed on the marked price.
ExplanationStatement I gives CP only. Statement II gives markup and discount rates but not CP. Together: MP = Rs. 1,000, SP = Rs. 900. -
DS2 Medium
During year-end stock clearance, management asks whether two counter sales together made money. Is the overall transaction profitable?
Statement ITwo items each costing Rs. 600 are sold at 15% profit and 15% loss respectively.
Statement IINo other costs are involved in either sale.
ExplanationTotal SP = 690 + 510 = Rs. 1,200 = total CP Rs. 1,200 → break even, not profitable. Statement I alone suffices.
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DS3 Hard
A store audit combines markup, discount, and false-weight adjustments on a single SKU. What is the final profit percentage on cost price?
Statement IThe cost price is Rs. 500 and the marked price is 40% above cost price.
Statement IIA discount of 20% is given on the marked price and false weight adds an effective 10% gain.
ExplanationMP = Rs. 700. SP from discount = Rs. 560. With 10% false-weight gain, effective revenue ≈ Rs. 616 → profit ≈ 23.2%. All three steps are needed. -
DS4 Hard
A pricing analyst must set the list price for a promotional offer on a new product line. What is the marked price?
Statement IThe cost price of each unit is Rs. 400.
Statement IIAfter a 10% discount on the marked price, the shopkeeper earns 8% profit on cost price.
ExplanationRequired SP = 432. MP = 432/0.90 = Rs. 480. Both statements are needed.