Percentage, Profit & Loss: Practice Questions with Answers

Percentages, profit and loss, discounts and successive changes. Try each question first: tap an option to check it, and the explanation appears below.

1. Question 1Medium

   By selling a shirt for ₹975, a shopkeeper loses 25%. What was the cost price?

   A.₹1,300B.₹1,000C.₹731.25D.₹1,218.75
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   ✅ A. ₹1,300

   A 25% loss means the selling price is 75% of the cost price. So cost price = ₹975 × 100 ÷ 75 = ₹1,300. Check: 25% of ₹1,300 is ₹325, and ₹1,300 − ₹325 = ₹975. Adding 25% to ₹975 gives ₹1,218.75, which is wrong because the loss is a percentage of the cost, not of the selling price.

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2. Question 2Hard

   The price of milk rises by 20%. By what percentage must a family reduce its consumption so that its spending on milk stays the same?

   A.20%B.10%C.16.67%D.25%
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   ✅ C. 16.67%

   Spending = price × quantity. Take the old price as 100 and the old quantity as 100, so the spending is 10,000. The new price is 120, so the quantity must become 10,000 ÷ 120 = 83.33. That is a cut of 16.67%. Shortcut: reduction % = rise ÷ (100 + rise) × 100 = 20 ÷ 120 × 100. Cutting by 20% would leave the family spending less than before.

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3. Question 3Hard

   A trader sells goods at the cost price but uses an 875 g weight in place of a 1 kg weight. What is the gain percentage?

   A.12.5%B.28.58%C.14.29%D.19.29%
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   ✅ C. 14.29%

   The buyer pays for 1,000 g but receives only 875 g. So the seller gains 125 g on every 875 g actually given. Gain % = (125 ÷ 875) × 100 = 14.29%. Dividing by 1,000 instead gives 12.5%, which is wrong because the cost is for the 875 g handed over.

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4. Question 4Hard

   A trader sells two chairs for ₹2,000 each. On one there is a profit of 30% and on the other a loss of 30%. What is the overall result?

   A.9% lossB.No profit, no lossC.9% profitD.30% loss
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   ✅ A. 9% loss

   The two cost prices are different. Cost of the first = ₹2,000 × 100 ÷ 130 = ₹1,538.46; cost of the second = ₹2,000 × 100 ÷ 70 = ₹2,857.14. Total cost ₹4,395.6 is more than the total selling price ₹4,000, so there is a loss of 9%. Shortcut: equal selling prices with x% profit and x% loss always give a loss of x²/100 %.

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5. Question 5Easy

   What is 15% of 4,840?

   A.726B.72.6C.4,114D.7,260
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   ✅ A. 726

   15% means 15 out of every 100. So 15% of 4,840 = 4,840 × 15 ÷ 100 = 726. A quick way: 1% of 4,840 is 48.4, and 15 times that is 726.

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6. Question 6Medium

   The price of a school bag is first increased by 40% and then decreased by 40%. What is the net change in its price?

   A.16% decreaseB.40% decreaseC.16% increaseD.No change
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   ✅ A. 16% decrease

   Take the price as 100. After a 40% increase it becomes 140. A 40% decrease is taken on 140, which is 56, so the price becomes 84. That is 16 less than the start: a net decrease of 16%. Shortcut: an equal rise and fall of x% always gives a decrease of x²/100 %.

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7. Question 7Easy

   What is 60% of 4,300?

   A.258B.25,800C.2,580D.1,720
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   ✅ C. 2,580

   60% means 60 out of every 100. So 60% of 4,300 = 4,300 × 60 ÷ 100 = 2,580. A quick way: 1% of 4,300 is 43, and 60 times that is 2,580.

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8. Question 8Medium

   The population of a town is 74,400. It grows by 5% every year. What will the population be after 2 years?

   A.81,840B.78,120C.82,770D.82,026
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   ✅ D. 82,026

   Each year's growth is on the new population. After 1 year: 74,400 × 105/100 = 78,120. After 2 years: 78,120 × 105/100 = 82,026. Adding 10% of the original once gives 81,840, which forgets the growth on the first year's increase.

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9. Question 9Hard

   A vendor sells two chairs for ₹600 each. On one there is a profit of 25% and on the other a loss of 25%. What is the overall result?

   A.25% lossB.No profit, no lossC.6.25% profitD.6.25% loss
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   ✅ D. 6.25% loss

   The two cost prices are different. Cost of the first = ₹600 × 100 ÷ 125 = ₹480; cost of the second = ₹600 × 100 ÷ 75 = ₹800. Total cost ₹1,280 is more than the total selling price ₹1,200, so there is a loss of 6.25%. Shortcut: equal selling prices with x% profit and x% loss always give a loss of x²/100 %.

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10. Question 10Medium

    Two successive discounts of 40% and 25% are equal to a single discount of:

    A.65%B.55%C.50%D.32.5%
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    ✅ B. 55%

    Take the price as 100. After 40% off it is 60. The second discount of 25% is on 60, which is 15, leaving 45. The total reduction is 55, so the single discount is 55%. Shortcut: a + b − ab/100 = 40 + 25 − 10 = 55%. Simply adding gives 65%, which is too high.

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11. Question 11Easy

    A shopkeeper buys a shirt for ₹1,700 and sells it at a profit of 20%. What is the selling price?

    A.₹340B.₹2,040C.₹1,720D.₹1,360
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    ✅ B. ₹2,040

    Profit is calculated on the cost price. Profit = 20% of ₹1,700 = ₹340. Selling price = cost price + profit = ₹1,700 + ₹340 = ₹2,040. Shortcut: selling price = cost × (100 + profit%) ÷ 100 = ₹1,700 × 120 ÷ 100.

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12. Question 12Easy

    What is 45% of 2,660?

    A.1,197B.119.7C.11,970D.1,463
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    ✅ A. 1,197

    45% means 45 out of every 100. So 45% of 2,660 = 2,660 × 45 ÷ 100 = 1,197. A quick way: 1% of 2,660 is 26.6, and 45 times that is 1,197.

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13. Question 13Hard

    A trader marks goods 60% above the cost price and then gives a discount of 25% on the marked price. What is the overall result?

    A.22% lossB.20% profitC.25% profitD.35% profit
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    ✅ B. 20% profit

    Take the cost price as 100. The marked price is 160. A 25% discount on 160 is 40, so the selling price is 120. Compared with the cost of 100, that is 20% profit. Subtracting the percentages (60 − 25 = 35) is a common mistake, because the discount is on the higher marked price.

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14. Question 14Hard

    In an examination, 19% of the students failed in English, 23% failed in Mathematics and 9% failed in both. What percentage of students passed in both subjects?

    A.9%B.58%C.67%D.49%
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    ✅ C. 67%

    Students who failed in at least one subject = failed in English + failed in Mathematics − failed in both (they were counted twice) = 19 + 23 − 9 = 33%. So the students who passed in both = 100 − 33 = 67%. Forgetting to subtract the 9% who failed in both gives 58%, which is too low.

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15. Question 15Easy

    A store owner buys a table lamp for ₹1,960 and sells it at a profit of 20%. What is the selling price?

    A.₹2,352B.₹392C.₹1,980D.₹1,568
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    ✅ A. ₹2,352

    Profit is calculated on the cost price. Profit = 20% of ₹1,960 = ₹392. Selling price = cost price + profit = ₹1,960 + ₹392 = ₹2,352. Shortcut: selling price = cost × (100 + profit%) ÷ 100 = ₹1,960 × 120 ÷ 100.

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16. Question 16Hard

    A store owner sells two chairs for ₹600 each. On one there is a profit of 10% and on the other a loss of 10%. What is the overall result?

    A.No profit, no lossB.1% profitC.10% lossD.1% loss
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    ✅ D. 1% loss

    The two cost prices are different. Cost of the first = ₹600 × 100 ÷ 110 = ₹545.45; cost of the second = ₹600 × 100 ÷ 90 = ₹666.67. Total cost ₹1,212.12 is more than the total selling price ₹1,200, so there is a loss of 1%. Shortcut: equal selling prices with x% profit and x% loss always give a loss of x²/100 %.

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17. Question 17Medium

    The population of a town is 16,600. It grows by 10% every year. What will the population be after 2 years?

    A.19,920B.20,086C.18,260D.20,252
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    ✅ B. 20,086

    Each year's growth is on the new population. After 1 year: 16,600 × 110/100 = 18,260. After 2 years: 18,260 × 110/100 = 20,086. Adding 20% of the original once gives 19,920, which forgets the growth on the first year's increase.

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18. Question 18Medium

    The price of a water bottle is first increased by 30% and then decreased by 30%. What is the net change in its price?

    A.9% decreaseB.No changeC.9% increaseD.30% decrease
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    ✅ A. 9% decrease

    Take the price as 100. After a 30% increase it becomes 130. A 30% decrease is taken on 130, which is 39, so the price becomes 91. That is 9 less than the start: a net decrease of 9%. Shortcut: an equal rise and fall of x% always gives a decrease of x²/100 %.

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19. Question 19Medium

    By selling a wristwatch for ₹720, a store owner loses 20%. What was the cost price?

    A.₹864B.₹900C.₹740D.₹576
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    ✅ B. ₹900

    A 20% loss means the selling price is 80% of the cost price. So cost price = ₹720 × 100 ÷ 80 = ₹900. Check: 20% of ₹900 is ₹180, and ₹900 − ₹180 = ₹720. Adding 20% to ₹720 gives ₹864, which is wrong because the loss is a percentage of the cost, not of the selling price.

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20. Question 20Hard

    A vendor sells goods at the cost price but uses a 960 g weight in place of a 1 kg weight. What is the gain percentage?

    A.8.34%B.4.17%C.9.17%D.4%
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    ✅ B. 4.17%

    The buyer pays for 1,000 g but receives only 960 g. So the seller gains 40 g on every 960 g actually given. Gain % = (40 ÷ 960) × 100 = 4.17%. Dividing by 1,000 instead gives 4%, which is wrong because the cost is for the 960 g handed over.

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