Percentage, Profit & Loss: previous-year questions

Answer: (C) She suffers a loss of 1%

When two articles are sold at the same selling price, one at a gain of $x\%$ and the other at a loss of $x\%$, there is always an overall loss of $\frac{x^2}{100}\%$. Here $\frac{10^2}{100} = 1\%$ loss. Check with numbers: if each goat sells for Rs 99, the cost prices are $\frac{99}{1.1} = 90$ and $\frac{99}{0.9} = 110$, total cost 200 against total sale 198, a loss of 2 on 200, i.e. $1\%$. The trap is option A: 'no profit, no loss' is true only when the two cost prices (not the selling prices) are equal.

Answer: (C) 30

Since the installments are equal and interest-free, 18 installments correspond to 60% of the loan, so the total number is $\frac{18}{0.60} = 30$. Each installment is therefore $\frac{100}{30} = 3\frac{1}{3}\%$ of the loan, and 12 installments (40%) remain. Unitary check: 60% is 18 installments, so 10% is 3 installments and 100% is 30. The other options fail the same check, since 60% of 22, 24 and 33 is 13.2, 14.4 and 19.8, not 18.

Answer: (A) 28 : 25

Take C = 100; then B = 80 and A = 80 × 1·4 = 112. So A : C = 112 : 100 = 28 : 25. Adding the percentages directly (40 − 20 = 20%) would wrongly suggest 6 : 5, and the other ratios do not fit.

Answer: (D) ₹ 1,089

Here the loss is 10% of the selling price, i.e. 10% of ₹ 990 = ₹ 99. So the cost price is 990 + 99 = ₹ 1,089. ₹ 1,100 would be the answer if the loss were 10% of the cost price, which is the usual trap.

Answer: (B) 75%

After the first discount the price is 50% of the original, and the second 50% leaves 25% of the original. The single equivalent discount is therefore 100 − 25 = 75%. Adding the two (100%) is the common mistake.

Answer: (C) ₹ 36

The question is meant as '4 eggs less are available for ₹ 24': a 50% price rise cuts what ₹ 24 buys by one-third, so those 4 eggs are one-third of the old quantity (12 eggs before, 8 eggs now). The present price is ₹ 24 ÷ 8 = ₹ 3 an egg, i.e. ₹ 36 a dozen. ₹ 24 was the old price per dozen, and ₹ 27 and ₹ 42 do not fit.

Answer: (A) 800

Going from a 20% loss to a 5% profit is a swing of 25% of the cost price, and this equals ₹ 200. So the cost price is 200 ÷ 0·25 = ₹ 800. ₹ 8,000 would need a swing of ₹ 2,000.

Answer: (C) −20%

Take the salary as 100: after a 50% cut it is 50, and a 60% rise makes it 80. The net change is 80 − 100 = −20%. Simply adding −50 and +60 gives the wrong +10%.

Answer: (C) $16\frac{2}{3}$%

Take the selling price as 100; the loss is 20, so the cost price is 120. Loss on cost price = 20 ÷ 120 × 100 = $16\frac{2}{3}$%. 25% is what a 20% gain on selling price would be on cost, a different situation.

Answer: (C) ₹ 80,000

Last year's tax was 4% of ₹ 1,00,000 = ₹ 4,000. For the same tax at 5%, income = 4000 ÷ 0·05 = ₹ 80,000. ₹ 1,25,000 reverses the ratio and would raise the tax.

Answer: (A) $9\frac{1}{11}$%

Reduction needed = $\frac{10}{100 + 10} \times 100 = \frac{100}{11} = 9\frac{1}{11}$%. A 10% cut is too much because it is measured on the old consumption. $11\frac{1}{9}$% is the extra consumption allowed when prices fall by 10%, a different case.

Answer: (C) 40% profit

With cost price 100, a 30% loss means a selling price of 70. Double that is 140, a profit of 40%. Doubling the 30% loss to 60% loss is the obvious trap.

Answer: (A) 40% loss

With a cost of 100, a 10% gain means a selling price of 110, and half of that is 55, so the sale ends in a heavy loss. Option (A) is the only large loss among the choices and is the answer in the key; it is exact if the original gain is 20%, since 120 ÷ 2 = 60. Worked with the printed 10%, the loss comes to 45%, which is not among the options, so the question appears to carry a misprint.

Answer: (D) 9·75

If $\frac{2}{3}$ of the number is 26, the number is 26 × $\frac{3}{2}$ = 39. 25% of 39 is 39 ÷ 4 = 9·75. The other decimals are near misses from rounding errors.

Answer: (B) $33\frac{1}{3}$

SP of 60 − CP of 60 = SP of 15, so CP of 60 articles = SP of 45 articles. The gain is the SP of 15 on a cost equal to the SP of 45, i.e. 15 ÷ 45 = $33\frac{1}{3}$%. 25% wrongly divides by 60 instead of 45.

Answer: (C) 25%

Purchase price = 800 × 0·9 × 0·85 = ₹ 612, and with ₹ 28 transport the cost is ₹ 640. Selling at ₹ 800 gives a gain of ₹ 160, i.e. 160 ÷ 640 = 25%. Ignoring the transport cost would give about 30·7%.

Answer: (D) $9\frac{1}{11}$%

Selling 110 mangoes brings in what 120 cost, so on 110 mangoes the gain equals the cost of 10. Gain % = 10 ÷ 110 × 100 = $9\frac{1}{11}$%. 10% wrongly divides by 100, and $11\frac{1}{9}$% by 90.

Answer: (A) 45:56

Selling price = 0·9 × printed price = 1·12 × cost price. So cost : printed = 0·9 : 1·12 = 90 : 112 = 45 : 56. The other ratios do not satisfy this equation.

Answer: (C) $66\frac{2}{3}$%

Take B = 100; then A = 60. B exceeds A by 40, which as a percentage of A is 40 ÷ 60 × 100 = $66\frac{2}{3}$%. 40% wrongly measures the difference against B.

Answer: (C) 400

The gap between 35% and 29% is 6% of the maximum, and it equals 24 marks. So the maximum is 24 ÷ 0·06 = 400. With 300 marks, 6% would be only 18.