Practice Questions
Concept Explanation
Many placement problems keep CP as the central unknown. Express SP, MP, profit, and loss in terms of CP, then solve.
If SP = 115% of CP and discount on MP is known, build: CP → MP → SP as multipliers on CP.
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Q1 EasyAn article costing Rs. 750 is sold at a loss of 20%. What is the selling price?ExplanationSP = 750 × (100 − 20)/100 = 750 × 0.80 = Rs. 600.
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Q2 EasyIf the cost price of an article is Rs. 240 and the selling price is Rs. 300, what is the profit percentage on cost price?ExplanationProfit = Rs. 60. Profit% = (60/240) × 100 = 25%.
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Q3 EasyA shopkeeper buys an item for Rs. 560 and sells it at a profit of 25%. What is the selling price?ExplanationSP = 560 × 1.25 = Rs. 700.
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Q4 EasyProfit on an article is 30% of the cost price. If the profit amount is Rs. 210, the cost price is:Explanation210 = 0.30 × CP → CP = 210/0.30 = Rs. 700.
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Q5 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 rupee. For 20% profit, SP = (1/6) × 1.20 = 1/5 rupee → 5 toffees per rupee.
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Q6 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 L milk + 20% water gives 1.2 L. CP per litre sold = 12/1.2 = Rs. 10. Profit = 15 − 10 = Rs. 5, which is 50% on CP.
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Q7 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/CP = 12/8 = 1.5. Gain% = (1.5 − 1) × 100 = 50%.
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Q8 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:ExplanationLet original price = P. 240/P − 240/(0.8P) = 6 → 240(1 − 1/0.8)/P = 6 → P = Rs. 10 per kg.
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Q9 MediumBy selling an article for Rs. 1,440, a man gains 20%. The cost price of the article is:ExplanationCP = SP × 100/(100 + 20) = 1440 × 100/120 = Rs. 1,200.
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Q10 MediumA trader sells goods at 15% profit on cost price. If the cost price is Rs. 680, the profit amount is:ExplanationProfit = 680 × 0.15 = Rs. 102.
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Q11 MediumAn article is sold for Rs. 920 at a profit of 15% on cost price. What is the cost price?ExplanationCP = 920 × 100/115 = Rs. 800.
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Q12 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. Original SP = 1.05x. New CP = 0.95x and new SP = 1.05x − 2 = 1.10(0.95x) → x = Rs. 400.
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Q13 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 = 1.3125/0.95 CP = 1.38158 CP. Profit without discount = 38.125% on CP.
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Q14 HardAn article is sold at a loss of 10%. If the selling price had been Rs. 90 more, there would have been a gain of 5%. The cost price is:Explanation0.90 CP + 90 = 1.05 CP → 90 = 0.15 CP → CP = Rs. 600.
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DS1 Easy
A retail trainee at the campus store must find the cost price of a single article sold during the day. What is the cost price of the article?
Statement IThe article is sold at a profit of 20% on cost price.
Statement IIThe profit amount on the sale is Rs. 140.
ExplanationTogether: CP = 140/0.20 = Rs. 700. Neither statement alone gives CP without the other quantity. -
DS2 Medium
During inventory reconciliation, the audit team needs the selling price of a marked-down item. What is the selling price?
Statement IThe cost price of the item is Rs. 800.
Statement IIThe shopkeeper earns a 12.5% profit on cost price.
ExplanationStatement I gives CP only; Statement II gives profit rate only. Together: SP = 800 × 1.125 = Rs. 900.
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DS3 Medium
A procurement analyst is reviewing a purchase record where marked price was not used in the transaction. What is the cost price of the article?
Statement IThe article is sold for Rs. 920 at a profit of 15% on cost price.
Statement IIMarked price is not involved in this transaction.
ExplanationStatement I alone: CP = 920/1.15 = Rs. 800. Statement II adds no numerical data. -
DS4 Hard
A store manager wants to know whether the article's cost exceeded Rs. 500 before approving a reorder. Is the cost price greater than Rs. 500?
Statement IThe article is sold for Rs. 660 at a profit of 10% on cost price.
Statement IIThe marked price is 20% above the cost price.
ExplanationStatement I alone: CP = 660/1.10 = Rs. 600, which exceeds Rs. 500.