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 Easy
An article bought for Rs. 400 is sold for Rs. 460. What is the profit percentage?
ExplanationProfit = 60. Profit% = (60/400) × 100 = 15%. -
Q2 Easy
If CP is Rs. 500 and loss is Rs. 50, what is the loss percentage?
ExplanationLoss% = (50/500) × 100 = 10%. -
Q3 Easy
At what price must an article costing Rs. 320 be sold to gain 25%?
ExplanationSP = 320 × 1.25 = Rs. 400. -
Q4 Medium
An article is sold at a loss of 8%. If CP is Rs. 750, what is SP?
ExplanationSP = 750 × 0.92 = Rs. 690. -
Q5 Medium
By selling an article for Rs. 1,440, a man gains 20%. The cost price is:
ExplanationCP = 1440 × 100/120 = Rs. 1,200. -
Q6 Medium
If SP is Rs. 870 and loss is 13%, CP is:
ExplanationCP = 870 × 100/87 = Rs. 1,000. -
Q7 Easy
Profit on an article is 30% of CP. If profit is Rs. 210, CP is:
Explanation210 = 0.30 × CP → CP = Rs. 700.
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Q8 Easy
Loss on an article is 12% of CP. If CP is Rs. 850, loss amount is:
ExplanationLoss = 850 × 0.12 = Rs. 102. -
Q9 Medium
A trader sells goods at 15% profit. If CP is Rs. 680, find profit amount.
ExplanationProfit = 680 × 0.15 = Rs. 102. -
Q10 Hard
If profit is 25% of SP (not CP), and SP is Rs. 500, profit amount is:
ExplanationProfit = 25% of SP = 0.25 × 500 = Rs. 100. Read the base carefully. -
Q11 Hard
An article is sold at 10% loss. If SP had been Rs. 90 more, there would be 5% profit. CP is:
Explanation0.9CP + 90 = 1.05CP → 90 = 0.15CP → CP = Rs. 600. -
Q12 Hard
By selling 33 articles, a vendor gets CP of 30 articles. Profit% is:
ExplanationProfit = 3 articles on CP of 30 → 3/30 × 100 = 10%. -
Q13 Hard
A man sells an article at 5% profit. If he bought it for 5% less and sold for Rs. 2 less, he would gain 10%. CP is:
ExplanationStandard result: CP = Rs. 400 (check: SP = 420; new CP = 380, new SP = 418 → 10% profit). -
Q14 Hard
If loss is one-third of SP, loss% on CP is:
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
What is the profit percentage?
Statement ICP is Rs. 600 and SP is Rs. 690.
Statement IIProfit 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.
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
What is the loss percentage?
Statement ISP is 90% of CP.
Statement IICP is Rs. 450.
ExplanationStatement I gives 10% loss. Statement II gives CP only. Together confirm loss% = 10% and CP = 450. -
DS4 Hard
Is the profit percentage greater than 20%?
Statement ISP is Rs. 1,200.
Statement IIProfit amount is Rs. 200.
ExplanationTogether: CP = 1000, profit% = 20%. Not greater than 20% — question is answerable.