Profit & Loss Questions and Answers

Answer: A

The profit is 10 %. Selling at 72 % of the selling price gives a loss of 12 %, so 0.72 of the selling price equals 0.88 of the cost price.

\[ 0.72\,SP = 0.88\,CP \Rightarrow SP = \frac{11}{9}\,CP \]

Selling at 10 % less than the original selling price gives 0.9 x (11/9) CP = 1.1 CP. That is a profit of 10 % on the cost price.

The options 12 %, 9 % and 8 % do not agree with 1.1 times the cost price, so the first option is the answer. As a check, take the cost price as 90. The selling price is then 110, and 72 % of 110 is 79.2, which is 12 % below 90. At 10 % less than 110, which is 99, the profit is 9 on 90, or 10 %.

Answer: C

The profit percent is 18.75 %. The article sells for 637.50 after a 15 % discount, so the list price L satisfies 0.85 L = 637.50, which gives L = 750.

\[ \text{SP at 5\% discount} = 0.95 \times 750 \]

\[ = 712.50 \]

\[ \frac{712.50 - 600}{600} \times 100 = 18.75\% \]

The options 15.5 %, 16.25 % and 19.5 % do not match 112.50 divided by 600, so the third option is correct. As a check, 85 % of the list price of 750 is 637.50, which agrees with the selling price given in the question. At a 5 % discount the price is 712.50, which is 112.50 above the cost.

Answer: C

He would gain 4%.

Selling at a 20% loss for 3000 means the cost price is 3000 / 0.8 = 3750.

\[ \text{gain}=3900-3750=150 \]

\[ \text{gain}\%=\frac{150}{3750}\times100=4\% \]

The 6% figures and the 4% loss do not match this working.

The 4% is a gain, not a loss, because 3900 is above the cost price of 3750. If the question had asked about a sale at 3,500, there would have been a loss. The 6% options come from using 3000 as the base instead of the cost price.

Answer: C

The rate is 20% per annum.

The cash price is 4400 and 2000 is paid at once, so 2400 is the outstanding amount. After one month 2440 is paid, so the interest is 40 on 2400 for one month, which is 1/60 of the amount per month.

\[ \frac{40}{2400}\times12\times100=20\% \]

10%, 15% and 25% would give a different monthly interest.

The buyer who pays by instalments gets the phone for 2000 now and 2440 later, a total of 4440 against the cash price of 4400. The extra 40 on the 2400 deferred is the interest for a month. A rate of 1/60 per month is 12/60 = 20% for a year.

Answer: A

The selling price is ₹30,430.

A 15% discount means the shopkeeper sells at 85% of the marked price.

\[ 35800\times0.85=30430 \]

₹30,340, ₹30,530 and ₹30,540 are not equal to 85% of 35,800.

Another way is to subtract the discount: 15% of 35,800 is 5,370 and 35,800 − 5,370 = 30,430. The other options are close to this but do not equal it.

Answer: C

His gain is 3 9/97 %.

He sells 970 g as 1000 g, so the goods that cost him for 970 g are sold for the price of 1000 g. The gain is the 30 g difference on the 970 g.

\[ \frac{30}{970}\times100=\frac{300}{97}=3\frac{9}{97}\% \]

The other options are not equal to 300/97.

This is a common result: when a dealer uses a false weight, the gain percentage is (error / true weight used) × 100. Here the error is 30 g and the weight actually given is 970 g, which gives 3 9/97%. Using 1000 g as the base would give 3%, which is not an option.

Answer: B

The final selling price is ₹12,000.

A double discount of 40% and 20% means the price is multiplied by 0.6 and then by 0.8.

\[ 25000\times0.6\times0.8=12000 \]

₹10,000 would come from a single discount of 60%, and ₹14,000 and ₹16,000 from smaller discounts.

The two discounts are not added: 40% + 20% = 60% would give 10,000. They are applied one after the other, so the price after the first is 15,000 and 20% off this is 3,000, leaving 12,000.

Answer: D

The cost price for Anuj is ₹5,200.

Nikunj paid 5,000 and sold at a 30% profit, so Sonia paid 6,500. Sonia sold at a 20% loss, so Anuj paid 80% of 6,500.

\[ 6500\times0.8=5200 \]

₹5,500 and ₹5,800 are not 80% of 6,500, and ₹5,000 would be the net result of a wrong cancellation.

Percent changes on successive sales apply to different bases. Nikunj's profit is on his own cost of 5,000 and Sonia's loss is on her cost of 6,500, so the final value is 6,500 × 0.8 = 5,200. Adding 30% and subtracting 20% on 5,000 would give 5,500, which is wrong.

Answer: D

The profit is 44%. Let the cost price be 100. Selling at \(\frac{23}{40}\) of the selling price gives a loss of 8%, so \[ \frac{23}{40}\,SP = 92 \] \[ SP = 92\times\frac{40}{23} = 160 \] At 90% of the original selling price: \[ 0.9\times 160 = 144 \] The profit is \(144 - 100 = 44\) on a cost of 100, which is 44%. The options 35%, 38% and 40% come from slipping on the fraction or on the 90%.

Answer: C

The selling price is ₹ 378. After the discount of \(x\)% and then 15%: \[ \begin{aligned} 450\times\left(1-\tfrac{x}{100}\right) &= \frac{351.90}{0.85} \\ &= 414 \end{aligned} \] \[ 1-\frac{x}{100} = \frac{351.90}{382.50} = 0.92 \] so \(x = 8\). A single discount of \(2x = 16\)% on the marked price gives \[ 450\times 0.84 = 378 \] ₹ 360 would be a 20% discount, ₹ 382.50 is only the 15% discount without the other, and ₹ 387.50 is not a whole-number discount of 450; only 378 matches.