Profit & Loss Questions and Answers

Answer: C

The person made a 1% loss.

Let each item sell for 100. The first was sold at a 10% profit, so it cost \(100/1.1 = 90.91\); the second at a 10% loss, so it cost \(100/0.9 = 111.11\).

\[ \begin{aligned} \text{cost} &= 90.91 + 111.11 = 202.02 \\ \text{loss} &= \frac{202.02 - 200}{202.02} \times 100 \approx 1\% \end{aligned} \]

The general rule: equal selling prices with equal percentage gain and loss of \(x\%\) always give a net loss of \(x^{2}/100\) percent, here \(10^{2}/100 = 1\%\). There is never a profit, which rules out both profit options, and 2% doubles the rule's result.

Answer: A

The profit is Rs. 0.

Rs. 100 at Rs. 50 a share buys 2 shares of A, and Rs. 80 at Rs. 80 buys 1 share of B, a total outlay of Rs. 180. The next day:

\[ \begin{aligned} \text{Value} &= 2 \times 55 + 1 \times 70 \\ &= 110 + 70 = 180 \\ \text{Profit} &= 180 - 180 = 0 \end{aligned} \]

The Rs. 10 gain on Stock A is exactly cancelled by the Rs. 10 loss on Stock B. Rs. 10 is the gain on Stock A alone, ignoring the Rs. 10 fall in Stock B, and Rs. 5 is the rise on a single share of A.

Answer: A

The actual profit was 5%.

Take the cost price as 100. The marked price includes 25% profit, and the discount is taken on the marked price.

\[ \begin{aligned} \text{MP} &= 100 \times 1.25 = 125 \\ \text{SP} &= 125 \times 0.84 = 105 \\ \text{profit} &= 105 - 100 = 5\% \end{aligned} \]

9% is the common mistake of subtracting the percentages (25 − 16), which ignores that the 16% is taken on 125, not on 100. 25% is the intended margin before any discount, and 16% is the discount itself.

Answer: B

The profit is 20%.

The milkman pays Rs. 1500 for 70 litres, adds 5 litres of water at no cost, and sells all 75 litres at Rs. 24 a litre:

\[ \begin{aligned} \text{SP} &= 75 \times 24 = 1800 \\ \text{Profit} &= 1800 - 1500 = 300 \\ \text{Profit \%} &= \frac{300}{1500} \times 100 = 20\% \end{aligned} \]

15% and 25% come from arithmetic slips, and 30% does not correspond to any reading of the data. Forgetting the water and selling only 70 litres would give Rs. 1680 and 12%, which is not offered.

Answer: C

The marked price is Rs. 43,750.

To gain 10% on a cost of Rs. 35,000, the selling price must be \(35000 \times 1.10 = 38500\). This selling price is the marked price less a 12% discount, so it is 88% of the marked price:

\[ \begin{aligned} 0.88 \times \text{MP} &= 38500 \\ \text{MP} &= \frac{38500}{0.88} = 43750 \end{aligned} \]

Check: 12% of 43,750 is 5,250, and 43,750 - 5,250 = 38,500, a gain of 3,500, which is 10% of 35,000. The other figures are close but give the wrong gain.

Answer: B

He spent ₹ 6,00,000 on the car.

A loss of 5% means the selling price is 95% of the cost price.

\[ \begin{aligned} 0.95 \times CP &= 5{,}70{,}000 \\ CP &= 6{,}00{,}000 \end{aligned} \]

Check: 5% of 6,00,000 is 30,000, and 6,00,000 − 30,000 = 5,70,000. Taking 5% of the selling price and adding it back gives 5,98,500, which is the classic mistake but not an option; 7,50,000, 5,00,000 and 4,50,000 do not give a 5% loss at all.

Answer: A

Only one statement is correct.

Statement 1: gain = 4,48,000 − 3,50,000 = 98,000, and \(98000 / 350000 = 28\%\). True.

Statement 2: cost per orange \(= 10/6 = 5/3\), selling price per orange \(= 6/4 = 3/2\). Loss per orange is \(5/3 - 3/2 = 1/6\), which is \(\tfrac{1/6}{5/3} = 10\%\), not 20%. False.

Statement 3: successive discounts of 12% and 5% leave \(0.88 \times 0.95 = 0.836\) of the price, so the original price is \(418 / 0.836 = 500\), not 250. False.

Answer: B

Rudra should choose the single discount of 30%.

Successive discounts are applied one after another, so the second acts on a reduced price. The net discount for successive rates \(a\) and \(b\) is \(a + b - ab/100\):

\[ \begin{aligned} 15, 15 &: 30 - 2.25 = 27.75\% \\ 20, 10 &: 30 - 2 = 28\% \\ 20, 12 &: 32 - 2.4 = 29.6\% \end{aligned} \]

All three successive offers fall short of a flat 30%, so 30% gives the maximum saving. The price of ₹ 11,212.32 is irrelevant, since every option is a percentage of the same price.

Answer: D

The seller bears a loss of 1%.

Take the cost price as 100. The marked price is 10% higher, and the selling price is 10% less than that:

\[ \begin{aligned} MP &= 100 \times 1.1 = 110 \\ SP &= 110 \times 0.9 = 99 \end{aligned} \]

Selling at 99 what cost 100 is a loss of 1%. 'No profit, no loss' is the trap: a 10% rise followed by a 10% cut does not return to the start, because the cut is taken on the larger figure. In general, \(x\%\) up then \(x\%\) down always gives a loss of \(x^{2}/100\) per cent.

Answer: C

The ratio Q : P is 6 : 7.

Take the cost price as 100. A 12% profit gives P = 112, and a 4% loss gives Q = 96:

\[ Q : P = 96 : 112 = 6 : 7 \]

Dividing both by 16 gives the simplest form. 4 : 5 and 1 : 1 do not match these prices, and 3 : 1 compares the percentages (12 and 4) instead of the prices.