Quantitative Aptitude

Profit, Loss and Discount

2,604 Questions
All Basic CP/SP Percentage Relationship 874 Marked Price, Markup, and Discount 786 Partial Sales and Multiple Transactions 338 Successive Discounts 218 Cost Price of X = Selling Price of Y 180 Faulty Weight or Measure 126 Equal Profit and Loss Rates 57 Free-item Offers 23 Price and Consumption Variation 1

Profit, Loss and Discount Questions

Multiple choice

A dealer allows a discount of 12% on the marked price. How much per cent above the cost price, must he mark his goods so as to make a profit of 10%?

  1. 18%

  2. 20%

  3. 24%

  4. 25%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CP = 100, MP = 100 + x. After 12% discount: SP = 0.88(100 + x). For 10% profit: SP = 110. So 0.88(100 + x) = 110, 100 + x = 125, x = 25%. The goods must be marked 25% above cost price. Verification: MP = 125, discount = 15, SP = 110, profit = 10 on CP = 100.

Multiple choice

If the cost price of a calculator becomes 3.2 times of itself and selling price also increases by 125\% then new profit percentage is 76\%. Find initial profit percentage?

  1. 130%

  2. 140%

  3. 165%

  4. 150%

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial CP = x, initial SP = y, initial profit = (y - x)/x = p%. New CP = 3.2x. New SP increases by 125%, so new SP = y + 1.25y = 2.25y. New profit% = (2.25y - 3.2x)/(3.2x) = 76. Substituting y = x(1 + p/100) and solving: 2.25x(1 + p/100) - 3.2x = 0.76 × 3.2x. Simplifying: 2.25 + 0.0225p - 3.2 = 2.432. So 0.0225p = 3.382, thus p = 130%.

Multiple choice

Discount given by a merchant on the marked price of goods is 25% more than the profit% earned on it. If discount is reduced by 20% profit is increased by 40% and becomes 28%. Find the actual cost price of the goods if the marked price is Rs 320.

  1. 200

  2. 220

  3. 260

  4. 280

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let profit% = p, discount% = d. Given d = 1.25p (25% more than profit). If discount reduced by 20%, new discount = 0.8d = 0.8(1.25p) = p. Profit increases by 40% and becomes 28%, so 1.4p = 28, giving p = 20%. Then d = 1.25 × 20 = 25%. Selling price at original discount = 320(1 - 0.25) = 240. Original profit = 20%, so Cost Price = 240/1.2 = 200. Verifying: If discount = 25%, SP = 320 × 0.75 = 240, Profit = 40, Profit% = 40/200 = 20%. Reduced discount = 25 × 0.8 = 20%, New SP = 320 × 0.8 = 256, New profit = 56, New profit% = 56/200 = 28% ✓.

Multiple choice

By selling an article for Rs 1134, Anu suffers as much loss as she would have gained by selling it at 10\% profit. If she sells it for Rs 1354.50, then her profit percentage is:

  1. 9

  2. 8

  3. 7.5

  4. 8.4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP be cost price. Loss at Rs 1134 = CP - 1134. This equals 10% profit = 0.1 × CP. So CP - 1134 = 0.1CP, meaning 0.9CP = 1134, giving CP = Rs 1260. When selling at Rs 1354.50, profit = 1354.50 - 1260 = Rs 94.50. Profit percentage = (94.50/1260) × 100 = 7.5%. The key insight is equating the loss amount to the 10% profit amount.

Multiple choice

Two shopkeepers sell the machines at the same marked price. The first shopkeeper allows two successive discounts of 30% and 6%, and the second shopkeeper allows 20% and 16%. Which discount series is most advantageous to the purchaser?

  1. First

  2. Second

  3. First = Second

  4. None of these

  5. Can’t be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For first series: 100 x 0.7 x 0.94 = 65.8, so 34.2% discount. For second series: 100 x 0.8 x 0.84 = 67.2, so 32.8% discount. The first series gives a lower final price (65.8 < 67.2), meaning more discount to the purchaser. Successive discounts compound, so order matters.

Multiple choice

If the profit on selling an article for Rs. 850 is the same as the loss on selling it for Rs. 710, then the cost price of the article is -

  1. Rs. 820

  2. Rs. 760

  3. Rs. 800

  4. Rs. 780
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let CP be the cost price. Profit at Rs. 850 = CP - 710. Setting them equal: 850 - CP = CP - 710, giving 2CP = 1560, so CP = 780. Option D is correct. At Rs. 820, profit would be 30 but loss would be 60 - not equal. Rs. 760 and 800 don't satisfy the equal profit-loss condition.

Multiple choice

A radio manufacturer fixed the marked price of radio as Rs. 325, enhancing 30% of the cost of production but allowed 12% discount to his customer during sale. The profit in this transaction is -

  1. Rs. 18

  2. Rs. 72

  3. Rs. 36

  4. Rs. 17.50
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Cost price = Rs. 325 / 1.30 = Rs. 250 (since marked price is 30% above cost). Selling price after 12% discount = Rs. 325 × 0.88 = Rs. 286. Profit = Selling Price - Cost Price = Rs. 286 - Rs. 250 = Rs. 36. This represents a 14.4% profit on cost.

Multiple choice

A person has bought two items P and Q. The purchase price of P was 75% of that of Q. He has sold P at a loss of 5% and Q at a profit of 15% and hence gets a total of Rs. 745 as the selling price of P and Q. Find the cost price of Q?

  1. 300

  2. 360

  3. 400

  4. 480

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Q's cost price = x. Then P's cost = 0.75x. P sold at 5% loss: 0.95 × 0.75x = 0.7125x. Q sold at 15% profit: 1.15x. Total SP = 0.7125x + 1.15x = 1.8625x = 745. Solving: x = 745/1.8625 = 400.

Multiple choice

The cost price of item B is Rs. 150 more than the cost price of item A. Item A was sold at a profit of 10% and item B was sold at a loss of 20%. If the respective ratio of selling prices of items A and B is 11: 12, what is the cost price of item B?

  1. Rs. 450

  2. Rs. 420

  3. Rs. 400

  4. Rs. 350

  5. Rs. 480
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let cost price of A = x. Then cost price of B = x+150. Selling price of A = 1.1x (10% profit). Selling price of B = 0.8(x+150) (20% loss). The ratio SP_A:SP_B = 11:12, so 1.1x / [0.8(x+150)] = 11/12. Cross-multiplying: 13.2x = 8.8x + 1320. Solving: 4.4x = 1320, x = 300. So CP of A = Rs. 300, and CP of B = 300+150 = Rs. 450. Therefore, the cost price of item B is Rs. 450.

Multiple choice

Abhi bought a certain quantity of oranges at total cost of Rs. 1200. He sold 1/3rd of those oranges at 20% loss. If Abhi earns an overall profit of 10%, at what profit percent did he sell the rest of the oranges?

  1. 16%

  2. 15%

  3. 22%

  4. 25%

  5. 20%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total cost = Rs. 1200. Cost of 1/3 oranges = 400, sold at 20% loss = 400 × 0.8 = Rs. 320. Cost of remaining 2/3 = 800. Overall 10% profit means total selling price = 1200 × 1.1 = Rs. 1320. Remaining oranges must sell for 1320 - 320 = Rs. 1000. Profit = (1000 - 800)/800 × 100 = 25%. Option D is correct.