Quantitative Aptitude

Profit, Loss and Discount: Practice Questions with Answers

14 practice questions on Profit, Loss and Discount, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   A shopkeeper buys a table for ₹1,200 and sells it for ₹1,500. Find his profit percentage.

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   Answer: 25%

   Solution:

   1. Profit = 1,500 − 1,200 = 300
   2. Profit% = (300 / 1,200) × 100
   3. = 25%

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2. Q.2

   A trader marks his goods 40% above cost price, then allows a discount of 10% on the marked price. Find his profit percentage.

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   Answer: 26%

   Solution:

   1. Let CP = 100. Marked Price = 100 × 1.40 = 140
   2. SP = 140 × (1 − 10/100) = 140 × 0.90 = 126
   3. Profit = 126 − 100 = 26, so Profit% = 26%
   4. Check with the successive-change formula: a=+40, b=−10 → net% = 40 − 10 + (40×−10)/100 = 30 − 4 = 26%.

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3. Q.3

   A dishonest dealer claims to sell rice at cost price but uses a weight of 800 g instead of 1 kg. Find his gain percentage.

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   Answer: 25%

   Solution:

   1. He charges the cost-price rate for 1,000 g but actually hands over only 800 g, so his real cost is only for 800 g.
   2. Let the price per gram equal his cost per gram, c. Revenue collected = 1,000c (he bills for 1 kg). Actual cost = 800c (what he really gave).
   3. Gain = 1,000c − 800c = 200c. Gain% on his actual cost = (200c / 800c) × 100
   4. = 25%

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4. Q.4

   An article marked at ₹2,000 is sold after a discount of 15%. Find the selling price.

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   Answer: ₹1,700

   Solution:

   1. SP = MP × (1 − 15/100)
   2. = 2,000 × 0.85
   3. = 1,700

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5. Q.5

   A man sells a watch for ₹1,140 at a loss of 5%. Find the cost price.

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   Answer: ₹1,200

   Solution:

   1. SP = CP × (1 − 5/100) = CP × 0.95
   2. 1,140 = CP × 0.95
   3. CP = 1,140 / 0.95 = 1,200

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6. Q.6

   A trader marks an item 25% above its cost price but still ends up making a profit of only 12.5% after a discount. Find the discount percentage.

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   Answer: 10%

   Solution:

   1. Let CP = 100, so MP = 125 and (since profit is 12.5%) SP = 112.5.
   2. Discount amount = MP − SP = 125 − 112.5 = 12.5
   3. Discount% = (12.5 / 125) × 100
   4. = 10%

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7. Q.7

   Two items are each sold for ₹1,200. On one, a shopkeeper gains 20%; on the other, he loses 20%. Find his overall loss or gain percentage on this pair.

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   Answer: 4% loss (not a break-even, even though the percentages look equal and opposite)

   Solution:

   1. CP of the first item = SP / 1.20 = 1,200 / 1.20 = 1,000.
   2. CP of the second item = SP / 0.80 = 1,200 / 0.80 = 1,500.
   3. Total CP = 1,000 + 1,500 = 2,500. Total SP = 1,200 + 1,200 = 2,400.
   4. Loss = 2,500 − 2,400 = 100. Loss% = (100 / 2,500) × 100 = 4%.
   5. Check against the identity: equal gain and loss of x% = 20% on equal selling prices always gives a loss of (x/10)% squared = (20/10)² = 4%. Matches.

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8. Q.8

   An item is marked up 40% above cost and then discounted by 20%. Find the net profit percentage.

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   Answer: 12%. Using net% = a + b + ab/100 = 40 − 20 + (40×−20)/100 = 20 − 8 = 12%.

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9. Q.9

   A man buys an item for ₹500 and sells it for ₹575. Find his profit percentage.

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   Answer: 15%. Profit = 75; 75/500 × 100 = 15%.

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10. Q.10

    A bicycle is sold at a loss of 12% for ₹2,640. Find its cost price.

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    Answer: ₹3,000. CP × 0.88 = 2,640, so CP = 2,640/0.88.

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11. Q.11

    A trader marks goods 20% above cost price and still makes a 4% profit after a discount. Find the discount percentage.

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    Answer: 13⅓%. MP = 120, SP = 104 (4% profit on CP 100); discount = 16 on MP 120, which is 16/120 × 100.

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12. Q.12

    A dealer professes to sell at cost price but uses a weight of 900 g for 1 kg. Find his gain percentage.

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    Answer: 11.1% (1/9 × 100%). Gain% = (1,000 − 900)/900 × 100.

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13. Q.13

    Goods marked at ₹800 are sold at a discount of 25%. Find the selling price.

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    Answer: ₹600. SP = 800 × 0.75.

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14. Q.14

    Two articles are each sold for the same price: one at a 10% gain, the other at a 10% loss. Find the overall loss percentage on the pair.

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    Answer: 1%. Using (x/10)² with x = 10: (10/10)² = 1%.

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