Profit & Loss Questions and Answers

Answer: D

The retailer makes a gain of 25%.

Let the marked price of one book be 1. The retailer pays the marked price of 32 books, that is 32, for 40 books, and sells all 40 at the marked price, receiving 40.

\[ \text{Gain} \% = \frac{40 - 32}{32} \times 100 = 25\% \]

Gain 20% divides the gain of 8 by the selling price of 40 instead of the cost of 32. There is no loss, since the retailer sells for more than he pays.

Answer: B

The additional discount is 12%.

After the 25% discount, the price is \(20000 \times 0.75 = 15000\). The further reduction needed is \(15000 - 13200 = 1800\), and as a percentage of the already discounted price:

\[ \frac{1800}{15000} \times 100 = 12\% \]

Successive discounts are taken on the reduced price, not the list price. 10% would leave the price at 13,500 and 18% at 12,300, and 32% treats the whole fall from 20,000 as a single further discount.

Answer: C

He spent ₹ 800 on repairs.

Let the purchase price be C. Repairs cost 0.2C, so his total cost is 1.2C. A 25% profit on that cost equals ₹ 1,200:

\[ \begin{aligned} 0.25 \times 1.2C &= 1200 \\ 0.3C &= 1200 \\ C &= 4000 \end{aligned} \]

Repairs = \(0.2 \times 4000 = 800\). Check: total cost 4800, selling price 6000, profit 1200, which is 25% of 4800.

The other figures fail the check: with repairs of ₹ 500 the purchase price would be 2,500 and the 25% profit 750, not 1,200.

Answer: A

He makes a profit of 6.5%.

Find each cost price first:

\[ \begin{aligned} CP_{A} &= \frac{384}{0{\cdot}8} = 480 \\ CP_{B} &= \frac{400}{1{\cdot}25} = 320 \\ \text{Total CP} &= 800 \\ \text{Profit} &= 852 - 800 = 52 \\ \text{Profit \%} &= \frac{52}{800} \times 100 = 6{\cdot}5\% \end{aligned} \]

The trap is to average the 20% loss and the 25% profit, or to work on selling prices instead of cost prices; neither gives the correct base of ₹ 800.

Answer: A

The profit would have been \(6\frac{2}{3}\)%.

A 24% discount means the selling price is 76% of the marked price:

\[ \begin{aligned} \text{MP} &= \frac{608}{0.76} = 800 \\ \text{Profit} &= 800 - 750 = 50 \\ \text{Profit \%} &= \frac{50}{750} \times 100 = 6\tfrac{2}{3} \end{aligned} \]

Dividing the profit by the marked price instead of the cost price gives 6.25%, which is not offered, and 6% is the figure rounded down; 5% and \(5\frac{1}{3}\)% do not follow from a marked price of ₹ 800.

Answer: A

His profit is ₹ 6.

Find each cost price from the selling price:

\[ \begin{aligned} CP_A &= \frac{348}{1.20} = 290 \\ CP_B &= \frac{348}{0.87} = 400 \\ \text{profit} &= 696 - 690 = 6 \end{aligned} \]

The total selling price is 2 × 348 = ₹ 696 and the total cost price ₹ 690. The trap is to work the percentages on the selling price: 20% of 348 minus 13% of 348 is about ₹ 24, not an option here, and averaging the percentages gives nothing meaningful either.

Answer: B

His overall profit is ₹ 20.

Find each cost price from the selling price of ₹ 850:

\[ \begin{aligned} CP_{1} &= \frac{850}{1.25} = 680 \\ CP_{2} &= \frac{850}{0.85} = 1000 \end{aligned} \]

\[ \begin{aligned} \text{Total CP} &= 680 + 1000 = 1680 \\ \text{Total SP} &= 2 \times 850 = 1700 \\ \text{Profit} &= 1700 - 1680 = 20 \end{aligned} \]

The trap is to take 25% and 15% of the same amount and conclude a 10% gain. The percentages apply to different cost prices, so the profit of ₹ 170 on the first article is almost cancelled by the loss of ₹ 150 on the second.

Answer: C

The profit is ₹ 250.

Apply the 20% discount to the marked price first, then the extra cash discount.

\[ \begin{aligned} \text{after 20\% off} &= 2500 \times 0.8 = 2000 \\ \text{selling price} &= 2000 - 250 = 1750 \\ \text{profit} &= 1750 - 1500 = 250 \end{aligned} \]

Taking the ₹ 250 off first and then 20% gives \(2250 \times 0.8 = 1800\), a profit of 300, which is the wrong order. Forgetting the cash discount altogether gives a profit of ₹ 500, which is not offered.

Answer: B

Her gain is 18%.

First find each cost price from its selling price.

\[ \begin{aligned} CP_A &= \frac{382.50}{0.85} = 450 \\ CP_B &= \frac{616}{1.12} = 550 \end{aligned} \]

Total cost is ₹ 1,000 and both articles together sell for ₹ 1,180, so the gain is ₹ 180.

\[ \text{Gain\%} = \frac{180}{1000} \times 100 = 18\% \]

The gain must be measured on the total cost of ₹ 1,000. The other options would need gains of ₹ 170, 175 or 165, which the prices given do not produce.

Answer: C

The cost price is ₹ 600.

First find the selling price after the 15% discount, then remove the 19% profit from it.

\[ \begin{aligned} \text{SP} &= 840 \times 0.85 = 714 \\ \text{CP} &= \frac{714}{1.19} = 600 \end{aligned} \]

Check: a 19% profit on ₹ 600 is ₹ 114, and \(600 + 114 = 714\).

A common slip is to take 19% off the selling price (\(714 \times 0.81 \approx 578\)), which lands near ₹ 580; profit is a percentage of the cost price, not of the selling price.