Profit & Loss Questions and Answers

Answer: A

He must sell the remaining land at 25% profit.

Let the whole field cost 1 (one unit). One-third and two-fifths are sold, so the rest is \(1 - \frac{1}{3} - \frac{2}{5} = \frac{4}{15}\). For a 10% overall profit, total sales must be 1.1:

\[ \begin{aligned} \tfrac{1}{3}(0.8) + \tfrac{2}{5}(1.25) &= \tfrac{4}{15} + \tfrac{1}{2} \\ &= \tfrac{23}{30} \\ \text{rest} &= 1.1 - \tfrac{23}{30} = \tfrac{1}{3} \\ \tfrac{1}{3} \div \tfrac{4}{15} &= 1.25 \end{aligned} \]

So the remaining land must fetch 1.25 times its cost, a profit of 25%. The lower options would leave the overall profit below 10%.

Answer: C

The selling price is ₹ 42,00,000.

The cost price includes the money spent on decoration:

\[ \begin{aligned} \text{CP} &= 27{,}75{,}000 + 2{,}25{,}000 = 30{,}00{,}000 \\ \text{SP} &= 30{,}00{,}000 \times \frac{140}{100} = 42{,}00{,}000 \end{aligned} \]

Applying the 40% profit to the purchase price alone gives about ₹ 38.85 lakh, which is not an option; ₹ 36,00,000 is a 20% profit, and ₹ 31,20,000 and ₹ 48,00,000 match no stated rate.

Answer: D

The profit is 5%.

If CP : SP = 20 : 21, take CP = 20 and SP = 21; the profit is 1 on a cost of 20.

\[ \text{profit}\% = \frac{1}{20} \times 100 = 5\% \]

Working the profit out on the selling price would give \(\frac{1}{21} \times 100 \approx 4.76\%\), not an option; 6¼%, 8% and 10% fit no step.

Answer: D

The gain is 25%.

Let the cost price of one article be Rs. 1. Then 12 articles sell for the cost of 15, Rs. 15, while they cost Rs. 12.

\[ \begin{aligned} \text{gain} &= 15 - 12 = 3 \\ \text{gain}\,\% &= \frac{3}{12} \times 100 = 25\% \end{aligned} \]

The common slip is to divide the gain by 15, the larger number, which gives 20%: gain per cent is always reckoned on the cost price of the articles actually sold, here 12. 10% and 15% match no step of the working.

Answer: A

The total profit is Rs. 25.

Find the total cost and the total selling price of the 150 bananas.

\[ \begin{aligned} \text{Cost} &= \frac{150}{2} \times 1 = \text{Rs. } 75 \\ \text{Sale} &= \frac{150}{3} \times 2 = \text{Rs. } 100 \\ \text{Profit} &= 100 - 75 = \text{Rs. } 25 \end{aligned} \]

Check: each banana costs 50 paise and sells for about 66.7 paise, a gain of one-sixth of a rupee per banana, and 150 bananas at one-sixth of a rupee is 25 rupees. The other options come from misreading the rates, for example treating '3 bananas in two rupees' as two rupees per banana.

Answer: A

The profit is 20%.

Profit percentage is always worked out on the cost price, so first find the cost price.

\[ \begin{aligned} \text{CP} &= 300 - 50 = \text{Rs. } 250 \\ \text{Profit \%} &= \frac{50}{250} \times 100 = 20\% \end{aligned} \]

The common mistake is to divide the profit by the selling price, which gives 50/300, about 16.7%, and is not offered. 25% would require a cost price of Rs. 200, and 10% or 5% would mean a far smaller profit on Rs. 250.

Answer: C

The loss is 10%.

Loss percent is always on the cost price. The cost price is the selling price plus the loss:

\[ \begin{aligned} CP &= 3600 + 400 = 4000 \\ \text{loss}\ \% &= \frac{400}{4000} \times 100 = 10 \end{aligned} \]

11% (more exactly 11.1%) comes from dividing the loss by the selling price, 3600, instead of the cost price. 15% and 8% match neither base.

Answer: C

Ravi bought the watch for Rs. 750.

A gain of 8% means the selling price is 108% of the cost price:

\[ \begin{aligned} 1.08 \times CP &= 810 \\ CP &= \frac{810}{1.08} = 750 \end{aligned} \]

Check: 8% of 750 is 60, and \(750 + 60 = 810\). The usual slip is to take 8% of the selling price, \(810 - 64.8 = 745.2\), which is not offered; 780, 760 and 786 give gains of under 4%, about 6.6% and about 3% respectively.

Answer: D

The profit earned is Rs. 180.

Let the cost price be C, so the marked price is C + 360. Profit is S - C and discount is (C + 360) - S, and they are equal.

\[ \begin{aligned} S - C &= C + 360 - S \\ 2S &= 2C + 360 \\ S - C &= 180 \end{aligned} \]

The 360 markup is split equally between discount and profit, Rs. 180 each, whatever the cost price.

Check with a cost of Rs. 1000: marked price 1360, selling price 1180, discount 180 and profit 180.

Answer: D

The gain is \(\frac{200}{17}\) per cent, about 11.76%.

Compare the same number of locks, the LCM of 8 and 12, which is 24:

\[ \begin{aligned} \text{CP of 24} &= 3 \times 34 = 102 \\ \text{SP of 24} &= 2 \times 57 = 114 \\ \text{gain} \% &= \frac{12}{102} \times 100 = \frac{200}{17} \end{aligned} \]

Equivalently, each lock costs Rs. 4.25 and sells for Rs. 4.75, a gain of Rs. 0.50 on 4.25. \(\frac{100}{17}\), about 5.9%, is half the true figure, and the other two options do not come from these prices.