Profit & Loss Questions and Answers

Answer: B

The added profit is ₹6,000 per month.

Old product: profit per unit = 75 - 60 = ₹15, so monthly profit = 15 × 1200 = ₹18,000.

New product: cost = 60 × 1.05 = ₹63, profit per unit = 75 - 63 = ₹12, so monthly profit = 12 × 2000 = ₹24,000.

Added profit = 24,000 - 18,000 = ₹6,000.

₹12,000 would be the result of ignoring the 5% cost rise (15 × 800 extra units), and ₹9,000 and ₹4,000 do not follow from either version of the calculation.

Answer: B

He should sell it for Rs 525.

Selling at Rs 475 means a 5% loss, so Rs 475 is 95% of the cost price:

\[ \begin{aligned} CP &= \frac{475}{0.95} = 500 \\ SP &= 500 \times 1.05 = 525 \end{aligned} \]

Rs 500 is the cost price itself, giving neither gain nor loss. Rs 535 and Rs 575 are gains of 7% and 15% on Rs 500. A common slip is adding 10% to Rs 475, which gives Rs 522.50 and is not an option.

Answer: D

The correct statement is that A makes a profit of 11%.

Let A's cost be Rs 100. A sells to B at 10% profit, for Rs 110. B sells it back at a 10% loss on Rs 110, for Rs 99.

\[ \begin{aligned} \text{A receives} &= 110, \quad \text{A pays} = 99 \\ \text{A's gain} &= 110 - 99 = 11 \end{aligned} \]

A ends with the item back and Rs 11 more than before, a profit of 11 on the original 100, which is 11%. A did not break even, and 20% comes from simply adding the two percentages. B lost Rs 11 on a Rs 110 outlay, which is 10%, not 20%.

Answer: A

The answer is ii: using 900 g of weight instead of 1 kg gives the most profit.

The options number the four methods i to iv in the order printed. Compare the profit of each on the cost of the sugar actually handed over:

• i: a 10% profit.
• ii: the customer pays for 1000 g but gets 900 g, so the profit is \(\frac{100}{900}\), about 11.1%.
• iii: adding 10% impurities to the sugar and selling at cost: 1.1 kg is sold for the cost of 1.1 kg of sugar while only 1 kg is sugar, a profit of 10%.
• iv: 5% more price for 5% less weight: \(\frac{1.05}{0.95}\), about 10.5%.

So method ii alone gives the most. The trap is in ii: cheating on weight by 10% yields more than 10% profit, because the gain is measured on the smaller quantity actually sold.

Answer: C

His profit is 8 %.

A 14% profit at a selling price of 2850 gives the cost price:

\[ \begin{aligned} \text{CP} &= \frac{2850}{1.14} = 2500 \\ \text{profit} &= 2700 - 2500 = 200 \\ \text{profit}\% &= \frac{200}{2500} \times 100 = 8 \end{aligned} \]

The discount only lowers the selling price to 2700, so the cost price stays 2500. Working the profit out on the selling price instead (200 out of 2700, about 7.4%) is the slip behind the 7% option.

Answer: B

The correct matching is a-II, b-IV, c-III, d-I.

• Profit percentage is profit over cost price: \(\frac{SP - CP}{CP} \times 100\) (II).
• Loss percentage is loss over cost price: \(\frac{CP - SP}{CP} \times 100\) (IV).
• Compound interest is the amount minus the principal: \(P\left(1 + \frac{r}{100}\right)^T - P\) (III).
• Simple interest is \(\frac{PRT}{100}\) (I).

Profit and loss are both calculated on the cost price; the only difference is which of SP and CP is larger, which is what separates II from IV.

Answer: D

The correct matching is a-III, b-I, c-II, d-IV.

Two successive discounts of \(x\%\) and \(y\%\) equal a single discount of \(x + y - \frac{xy}{100}\) percent:

\[ \begin{aligned} \text{a: } 10 + 5 - 0.5 &= 14.5\% \\ \text{b: } 15 + 4 - 0.6 &= 18.4\% \\ \text{c: } 20 + 10 - 2 &= 28\% \\ \text{d: } 12 + 8 - 0.96 &= 19.04\% \end{aligned} \]

Simply adding the two discounts (15%, 19%, 30%, 20%) overstates each one, because the second discount applies to an already reduced price.

Answer: D

The selling price would be ₹ 450.

After a 20% discount the item sells for 80% of its marked price:

\[ \begin{aligned} 0.8 \times MP &= 400 \\ MP &= 500 \\ 0.9 \times 500 &= 450 \end{aligned} \]

With only a 10% discount, the selling price is 90% of ₹ 500. The trap is to add 10% of ₹ 400 to get ₹ 440; the discount is always worked on the marked price, not on the selling price.

Answer: D

The profit is ₹ 350.

Let the cost price be C. The marked price is 1.25C, and after a 12% discount the selling price is 88% of that:

\[ \begin{aligned} SP &= 1.25C \times 0.88 = 1.1C \\ 1.1C &= 3850 \\ C &= 3500 \\ \text{profit} &= 3850 - 3500 = 350 \end{aligned} \]

So the overall profit is 10% of the cost. The common slip is to treat the net gain as 25% − 12% = 13%; successive percentage changes multiply, and 1.25 × 0.88 = 1.10, a gain of 10%.

Answer: D

The quantity sold at 18% profit is 48 kg.

By alligation, the two parts are in the ratio of the differences from the average profit of 14%:

\[ \begin{aligned} 8\% : 18\% &= (18 - 14) : (14 - 8) \\ &= 4 : 6 = 2 : 3 \\ \text{at } 18\% &= \tfrac{3}{5} \times 80 = 48 \end{aligned} \]

Check: 32 kg at 8% and 48 kg at 18% give an average of \(\frac{32 \times 8 + 48 \times 18}{80} = 14\%\). 32 kg is the part sold at 8%, which is the trap.