Profit & Loss Questions and Answers

Answer: A

The profit is 50%.

Take the cost price as 100. With a 25% discount the profit is 25%, so the selling price is 125, which is 75% of the marked price:

\[ \begin{aligned} 0.75\,MP &= 125 \Rightarrow MP = 166.67 \\ 0.90\,MP &= 150 \end{aligned} \]

Selling at 150 what cost 100 is a profit of 50%. 40% is the trap: adding the 15-point reduction in discount directly to the profit ignores that the discount is a percentage of the marked price, not of the cost.

Answer: B

The profit is 10%.

Take the market price of one pen as 1. The retailer pays the price of 36 pens for 40, and sells each at 1% below the market price:

\[ \begin{aligned} CP &= 36/40 = 0.90 \\ SP &= 0.99 \\ \text{profit} &= 0.09/0.90 = 10\% \end{aligned} \]

11% is the profit without the discount (4/36), and 9% comes from dividing the gain by the selling price instead of the cost.

Answer: A

The original cost of the treadmill is Rs. 12,500.

Selling at a 6% loss and selling at a 4% gain differ by 10% of the cost price, and that difference is the extra Rs. 1,250.

\[ \begin{aligned} (4\% + 6\%) \times C &= 1250 \\ 0.10\,C &= 1250 \\ C &= 12500 \end{aligned} \]

Check: a 6% loss gives Rs. 11,750 and a 4% gain gives Rs. 13,000, which differ by Rs. 1,250. Note that 11,750 and 13,000 among the options are those two selling prices, not the cost.

Answer: B

The overall profit is 33.33%.

Treat the two deals as one: add up everything paid and everything received.

\[ \begin{aligned} \text{cost} &= 15 + 30 = 45\ \text{lacs} \\ \text{sale} &= 20 + 40 = 60\ \text{lacs} \\ \text{profit} &= \frac{15}{45} \times 100 = 33.33\% \end{aligned} \]

Each deal on its own also gives a third: a profit of 5 on 15 and of 10 on 30, both 33.33%, which confirms the result. The other options differ only in the whole number and do not come from this calculation.

Answer: C

The cost price is Rs. 74,000.

Let the cost price be \(C\). The loss at Rs. 70,000 is \(C - 70000\), and the gain at Rs. 82,000 is twice that loss:

\[ \begin{aligned} 82000 - C &= 2(C - 70000) \\ 82000 + 140000 &= 3C \\ C &= 74000 \end{aligned} \]

Check: the loss is Rs. 4,000 and the gain Rs. 8,000, double the loss. 73,000 would make the gain 9,000 against a loss of 3,000, three times rather than twice.

Answer: A

The cost price was Rs. 500.

Selling at a 10% loss gives 0.9 of the cost price, and selling at a 10% profit gives 1.1 of it. The two prices differ by Rs. 100.

\[ \begin{aligned} 1.1C - 0.9C &= 100 \\ 0.2C &= 100 \\ C &= 500 \end{aligned} \]

Check: Rs. 450 is a 10% loss on 500, and Rs. 550 is a 10% profit; the gap is Rs. 100. The other options give gaps of Rs. 120, 140 and 160, since the gap is always 20% of the cost price.

Answer: C

The fourth shirt was sold at an 11.5% profit.

Take the cost of each shirt as 100, so the four cost 400. A 6% overall profit means total sales of 424.

\[ \begin{aligned} 2 \times 110 + 92.5 &= 312.5 \\ 424 - 312.5 &= 111.5 \end{aligned} \]

The fourth shirt sold for 111.5 against a cost of 100, an 11.5% profit. The first three shirts together earn only 12.5 on a cost of 300, about 4.2%, which is below the 6% target, so the fourth must be sold at more than 6% profit; that rules out both loss options and the 3.5% profit.

Answer: B

His gain percent is 20%.

The repair cost is part of the cost price:

\[ \begin{aligned} \text{CP} &= 11500 + 1000 = 12500 \\ \text{Gain} &= 15000 - 12500 = 2500 \\ \text{Gain}\% &= \frac{2500}{12500} \times 100 = 20\% \end{aligned} \]

Since he sold for more than he spent, there is no loss, which rules out both loss options. Ignoring the repair cost would give a gain of 3500 on 11500, about 30%, which is not offered; 15% has no basis in these figures.

Answer: D

The purchase price is ₹ 10,000.

A profit of 12 per cent means the selling price is 112 per cent of the cost price:

\[ \begin{aligned} \text{CP} &= \frac{11200 \times 100}{112} \\ &= 10000 \end{aligned} \]

Check: 12 per cent of 10,000 is 1,200, and 10,000 + 1,200 = 11,200. The trap is to take 12 per cent of the selling price instead of the cost price; 9,000, 9,500 and 9,600 all give profits that are not 12 per cent of their own cost.

Answer: A

The cost price is Rs. 200.

Find the selling price after the discount, then remove the 12% profit.

\[ \begin{aligned} \text{SP} &= 280 \times 0.8 = 224 \\ \text{CP} &= \frac{224}{1.12} = 200 \end{aligned} \]

Check: a 12% profit on Rs. 200 is Rs. 24, giving Rs. 224, which is 20% off Rs. 280. The other values come from subtracting percentages directly from the marked price instead of working through the selling price.