Profit & Loss Questions and Answers

Answer: A

The discount is 10/3 per cent. The discount is 1500 - 1450 = 50 rupees, and as a percentage of the marked price \[ \frac{50}{1500} \times 100 = \frac{10}{3}\% \] which is 3 1/3 per cent.

12/5, 14/5 and 8/3 per cent would be discounts of 36, 42 and 40 rupees, not 50.

Answer: B

His total profit is 33.33 per cent. Using a weight 10% short means he hands over 900 g for every 1000 g he charges for. He also prices at 20% above cost, so for goods that cost him 900 g worth (cost 900 units) he receives 1.2 × 1000 = 1200 units. \[ \text{Profit} = \frac{1200 - 900}{900} \times 100 = 33.33\% \]

33%, 34% and 34.33% are rounding or arithmetic slips of this figure.

Selling at a weight less by 10 per cent adds a gain of 100/9 per cent on cost price, about 11.11 per cent, on top of the stated profit of 20 per cent.

Answer: D

Four pairs can be bought. A dozen pairs costs 80 rupees, and after a 10% discount it costs 72 rupees, so one pair costs 72 / 12 = 6 rupees. Then 24 / 6 = 4 pairs.

Without the discount a pair would cost about 6.67 rupees and 24 rupees would buy only 3 whole pairs, which is the trap in option 3. Options 12 and 13 ignore the price per pair altogether.

Another way to see it: after the 10% discount the dozen costs 72 rupees, so one pair costs 6 rupees, and 24 rupees buys four pairs.

Answer: B

The gain is 6.425 per cent. Let the cost price be 100. The marked price is 110. A discount of 3 1/4 per cent leaves 96.75 per cent of it: \[ SP = 110 \times 0.9675 = 106.425 \] so the gain is 6.425 on 100, which is 6.425 per cent.

5.425, 7.425 and 8.425 per cent would need a selling price different from 106.425.

Answer: B

The original price is Rs 1,500. A 10 per cent rise followed by a 10 per cent fall leaves the price at 1.1 x 0.9 = 0.99 of the original, so the original price is 1485 / 0.99 = 1500. Rs 1,450 would give 1435.5 and Rs 1,550 would give 1534.5; Rs 1,650 is the price after only the 10 per cent rise. The two successive changes are not equal to zero overall, since 10 per cent of a larger number is more than 10 per cent of the original. The net effect is a fall of 1 per cent: 1500 becomes 1650 after the rise and 1485 after the fall, which matches the given latest price.

Answer: C

The profit is Rs 10,000 on a cost price of Rs 50,000, so the profit percentage is 10000/50000 x 100 = 20 per cent. 10 per cent would be a profit of Rs 5,000, 15 per cent Rs 7,500 and 25 per cent Rs 12,500. Profit percentage is always taken on the cost price, so the base is Rs 50,000 and not the selling price. Using Rs 60,000 as the base would give 16.67 per cent, which is not an option.

Answer: C

A 20 per cent discount leaves 80 per cent of the marked price, so the selling price is 0.8 x 2220 = Rs 1,776. Rs 1,976, Rs 1,876 and Rs 1,676 correspond to discounts of about 11, 15.5 and 24.5 per cent. The discount is 20 per cent of Rs 2,220, which is Rs 444, and 2220 minus 444 is 1776. The same result comes from multiplying by 4/5, since 2220 divided by 5 is 444 and 444 times 4 is 1776.

Answer: B

Successive discounts of x per cent and y per cent leave (1 - x/100)(1 - y/100) of the price, which equals 1 - (x + y - xy/100)/100. So the single equivalent discount is (x + y - xy/100) per cent. The options with x - y or a plus sign before xy/100 do not come from this product. With x = 10 and y = 20 the combined discount is 10 + 20 - 2 = 28 per cent. Directly, 0.9 x 0.8 = 0.72, so the discount is 28 per cent, which confirms that the product term xy/100 is subtracted.

Answer: A

The discount is the marked price less the selling price, Rs. 2500 - Rs. 2200 = Rs. 300. The discount percentage is always worked on the marked price, not on the selling price, so it is 300 / 2500 x 100 = 12 percent. As a check, 12 percent of Rs. 2500 is Rs. 300, and Rs. 2500 less Rs. 300 gives the selling price of Rs. 2200. So the answer is 12 percent, option (A). The values 15, 10 and 20 percent do not equal 300 divided by 2500; 15 percent would give a discount of Rs. 375.

Answer: C

Suppose he bought n oranges of each kind. At 3 oranges per rupee the first lot cost n/3 rupees, and at 2 oranges per rupee the second lot cost n/2 rupees, so the total cost is 5n/6. He had 2n oranges, sold at 5 for Rs. 2, which brings 2n x 2/5 = 4n/5. The loss is 5n/6 - 4n/5 = n/30, and this equals Rs. 3, so n = 90. He bought 90 + 90 = 180 oranges, option (C). The value 90 is the number of each kind, and 150 and 300 do not give a loss of Rs. 3.