Profit & Loss Questions and Answers

Answer: A

Let the marked price be M. Ayush buys the pen at a 10 per cent discount, so his cost price is 0.9M. He sells it at a 20 per cent profit for 405 rupees.

\[ 1.2 \times 0.9M = 405 \Rightarrow 1.08M = 405 \]

\[ M = \frac{405}{1.08} = 375 \]

So the marked price is 375 rupees. Check: the cost is 337.5, and 20 per cent more is 405. The values 370.50, 360 and 360.50 do not satisfy this. The answer is 375 rupees, option A.

Answer: B

The profit is 25 per cent. The cost price includes the repair expense: 225 + 15 = 240 rupees. The selling price is 300 rupees, so the profit is 300 - 240 = 60 rupees. The profit percent is \[\frac{60}{240} \times 100 = 25\] If only the purchase price 225 were used as the cost, the figure would be 33.3 per cent, which is not among the options, and the other options 20, 24 and 30 per cent do not result from either base.

Answer: D

The single discount is 23.5 per cent. After successive discounts of 10 and 15 per cent the price becomes 0.90 x 0.85 = 0.765 of the original, so the total discount is 1 - 0.765 = 0.235, which is 23.5 per cent. Equivalently, the single discount is \[10 + 15 - \frac{10 \times 15}{100} = 23.5\] per cent. The option 25 per cent just adds the two discounts and ignores the second being taken on the reduced price.

Answer: B

The cost of the item is Rs. 116.13 (to the nearest paisa). With a 10 per cent discount on the MRP of Rs. 140 the selling price is 140 x 0.90 = Rs. 126. A profit of 8.5 per cent means selling price = 1.085 x cost, so \[\text{cost} = \frac{126}{1.085} \approx 116.13\] The options 129.30, 126.30 and 113.13 do not satisfy this: for example a cost of 113.13 would give a profit of 11.4 per cent.

Answer: B

The discount is the marked price minus the selling price, and the rate is the discount as a fraction of the marked price.

\[ \frac{720-500}{720} \times 100 = \frac{220}{720} \times 100 \]

\[ = \frac{275}{9}\% \]

The rate of discount is 275/9 per cent, about 30.6 per cent. The other options are values of more than 30 per cent that are much higher or lower than this.

Answer: B

The profit is 3.49 per cent. Take the cost price as 100. The marked price is 31 per cent more, which is 131. A discount of 21 per cent leaves 79 per cent of the marked price.

\[ SP = 131 \times 0.79 = 103.49 \]

\[ \text{profit} = 103.49 - 100 = 3.49 \Rightarrow 3.49\% \]

Because the cost price was taken as 100, the profit figure is already a percentage. The options 2.85, 4.15 and 1.85 would come from using a wrong discount factor, such as 0.78 or 0.8, or a wrong marked price.

Answer: C

The profit is 60 per cent. Let the marked price be 100, so the cost price is 50. A discount of 20 per cent gives a selling price of 80.

\[ \text{profit} = 80 - 50 = 30 \]

\[ \text{profit \%} = \frac{30}{50} \times 100 = 60\% \]

Profit percent is always taken on the cost price, not on the marked price. The figure 50 per cent would be the profit with no discount, since 100 against 50 gives 50 on 50 or 100 per cent, not 50. The options 48 and 52 do not follow from the data.

Answer: A

The profit rises by 5 percentage points. At 10% profit on Rs 200 the selling price is Rs 220. At a selling price of Rs 230 the profit is Rs 30, which is

The profit percentage therefore goes from 10% to 15%, an increase of 5%. 10%, 15% and 20% are the old rate, the new rate and an unrelated value, not the increase.

A common error is to answer 10% by dividing the extra Rs 10 by Rs 100 or to answer 15% by quoting the new profit. The question asks for the increase in the profit per cent, which is the difference of the two percentages, 15 - 10 = 5 percentage points.

Answer: B

The single equivalent discount is 32%. For successive discounts of 20% and 15% the price falls to 0.8 × 0.85 of the marked price.

Adding the two percentages gives 35%, which ignores that the second discount is on the reduced price, so 35% is wrong, and 15% and 5% do not match either.

Check with a marked price of Rs 100: after 20% off the price is Rs 80, and after 15% off Rs 80 it is Rs 68. The total reduction is Rs 32 on Rs 100, which is 32%. The shortcut formula is a + b - ab/100 = 20 + 15 - 3 = 32.

Answer: C

The selling price is Rs 363.375. After three successive discounts of 15%, 10% and 5%, the price is the marked price times 0.85, 0.90 and 0.95.

364.375 and 333.375 differ in a digit or a stage, and 36.3375 is off by a factor of ten.

Check by the shortcut: the three multipliers are 0.85, 0.90 and 0.95, and their product is 0.72675, so the price is 500 × 0.72675 = 363.375. Option D, 364.375, is a plausible slip of a digit, and the single equivalent discount is 27.325 percent, not the 30 percent obtained by adding the three rates.