Practice Questions
Concept Explanation
Profit% and loss% compare the gain or loss to the cost price. This is the standard rule in placement papers unless the question says otherwise.
Formulas
- Profit% = (Profit / CP) × 100
- Loss% = (Loss / CP) × 100
- SP when profit is p%: SP = CP × (100 + p) / 100
- CP when profit is p% and SP is known: CP = SP × 100 / (100 + p)
Reverse Problems
If an article is sold at x% profit, CP is 100/(100 + x) of SP. At x% loss, CP is 100/(100 − x) of SP.
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Q1 EasyAn article is sold at a loss of 10%. If the selling price is Rs. 450, the cost price is:ExplanationCP = 450 × 100/(100 − 10) = 450 × 100/90 = Rs. 500.
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Q2 EasyDuring an aptitude screening, a candidate finds that an article costing Rs. 750 is sold at a profit of 20%. What is the selling price?ExplanationSP = 750 × 1.20 = Rs. 900.
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Q3 MediumThe cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:Explanation20 CP = x SP and SP = 1.25 CP → 20 = 1.25x → x = 16.
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Q4 MediumBy selling 33 articles, a shopkeeper gains the cost price of 11 articles. His gain percent is:ExplanationProfit = 11 articles on CP of 33 articles. Gain% = (11/33) × 100 = 33 1/3%.
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Q5 MediumSome articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:ExplanationCP per article = 5/6 and SP per article = 6/5. Gain% = ((6/5 − 5/6)/(5/6)) × 100 = 44%.
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Q6 MediumBy selling an article for Rs. 720, a man gains 20%. The cost price of the article is:ExplanationCP = 720 × 100/(100 + 20) = Rs. 600.
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Q7 MediumAn article is sold for Rs. 575 at a profit of 15% on cost price. What is the cost price of the article?ExplanationCP = 575 × 100/115 = Rs. 500.
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Q8 MediumBy selling an article for Rs. 1,035, a shopkeeper gains 15% on the cost price. What is the profit amount?ExplanationCP = 1035/1.15 = Rs. 900. Profit = 1035 − 900 = Rs. 135.
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Q9 MediumIf the profit on an article is 25% of the cost price and the profit amount is Rs. 175, what is the selling price?ExplanationCP = 175/0.25 = Rs. 700. SP = 700 + 175 = Rs. 875.
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Q10 HardA man buys an article for 10% less than its value and sells it for 10% more than its value. His gain or loss percent is:ExplanationCP = 0.9V and SP = 1.1V. Profit% on CP = (0.2V/0.9V) × 100 = 22 2/9% gain.
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Q11 HardIn a quantitative aptitude drill, an article sold at 5% loss would fetch Rs. 38 less than when sold at 10% profit. What is the cost price?Explanation1.10CP − 0.95CP = 38 → 0.15CP = 38 → CP = Rs. 380.
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Q12 HardA shopkeeper sells two similar articles, each with cost price Rs. 800, one at 25% profit and the other at 25% loss. What is the overall profit or loss percentage on the combined cost price?ExplanationTotal CP = Rs. 1,600. Total SP = 1000 + 600 = Rs. 1,600. Net result is break-even.
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Q13 HardAn article is sold at 10% loss. If the selling price had been Rs. 90 more, there would have been 5% profit. What is the cost price?Explanation0.90CP + 90 = 1.05CP → 90 = 0.15CP → CP = Rs. 600.
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Q14 HardIf loss is one-third of the selling price, what is the loss percentage on cost price?ExplanationLoss = SP/3 and CP = SP − SP/3 = 2SP/3. Loss% on CP = (SP/3)/(2SP/3) × 100 = 50%.
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DS1 Easy
In an aptitude screening test, candidates must find the profit percentage on cost price. What is the profit percentage?
Statement IThe cost price is Rs. 600 and the selling price is Rs. 690.
Statement IIThe profit amount is Rs. 90.
ExplanationStatement I: (90/600) × 100 = 15%. Statement II alone lacks CP. -
DS2 Medium
What is the cost price?
Statement IThe article is sold at 20% profit on cost price.
Statement IIThe selling price is Rs. 960.
ExplanationStatement I alone lacks SP. Statement II: CP = 960/1.2 = Rs. 800.
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DS3 Medium
In a profit-loss drill, what is the loss percentage reckoned on cost price?
Statement IThe selling price is 90% of the cost price.
Statement IIThe cost price is Rs. 450.
ExplanationStatement I gives 10% loss. Statement II gives CP only. Together confirm loss% = 10% and CP = Rs. 450. -
DS4 Hard
An HR analytics case study asks whether the profit percentage exceeds 20%. Is the profit percentage greater than 20%?
Statement IThe selling price is Rs. 1,200.
Statement IIThe profit amount is Rs. 200.
ExplanationTogether: CP = Rs. 1,000 and profit% = 20%. The question is answerable: profit is not greater than 20%.