Profit & Loss Questions and Answers

Answer: C

The gain is 20%.

Find the cost and selling price of one orange:

\[ \begin{aligned} \text{CP} &= \frac{1}{2} = 0.50 \\ \text{SP} &= \frac{3}{5} = 0.60 \\ \text{gain} &= \frac{0.10}{0.50} \times 100 = 20\% \end{aligned} \]

Equivalently, 10 oranges cost Rs. 5 and sell for Rs. 6. Measuring the gain of 10 paise against the selling price instead gives about 16.7%, which is not offered.

Taking the LCM of 2 and 5, ten oranges cost Rs. 5 and sell for Rs. 6, a gain of Re. 1 on Rs. 5, which is the same 20%.

Answer: D

The cost price is Rs. 45,000.

A 20% gain means the selling price is 120% of the cost price:

\[ \begin{aligned} 1.2 \times \text{CP} &= 54000 \\ \text{CP} &= 45000 \end{aligned} \]

Check: 20% of 45,000 is 9,000, and 45,000 + 9,000 = 54,000. Rs. 43,200 would come from wrongly taking 20% off the selling price, and the other options do not give a 20% gain.

In general, \(\text{CP} = \text{SP} \times \frac{100}{100 + \text{gain}\%}\), here \(54000 \times \frac{100}{120} = 45000\).

Answer: A

The gain is 20%.

If SP is \(\frac{6}{5}\) of CP, the gain is \(\frac{6}{5} - 1 = \frac{1}{5}\) of CP.

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

For instance, if the cost price is Rs. 100 the selling price is Rs. 120, a gain of Rs. 20 on Rs. 100. Working the gain out on the selling price instead would give about 16.7%, which is not offered, and 25%, 30% and 24% fit no step of the working.

Answer: C

The profit percentage is 20%.

Profit percentage is calculated on the cost price:

\[ \begin{aligned} \text{Profit} &= 960 - 800 = 160 \\ \text{Profit \%} &= \frac{160}{800} \times 100 = 20\% \end{aligned} \]

A common slip is to divide by the selling price: 160/960 is about 16.7%, which is not offered. 15%, 18% and 25% correspond to profits of ₹ 120, ₹ 144 and ₹ 200 on ₹ 800, not ₹ 160.

Answer: B

The selling price is ₹ 600.

A discount is taken on the marked price:

\[ \begin{aligned} \text{Discount} &= 20\% \text{ of } 750 = 150 \\ \text{SP} &= 750 - 150 = 600 \end{aligned} \]

Equivalently, the customer pays 80% of the marked price, and 0.8 times 750 is 600.

₹ 625 would be a discount of about 16.7%, ₹ 650 a discount of about 13.3%, and ₹ 580 a discount of about 22.7%, none of which is 20%.

Answer: A

The overall profit is \(15\frac{5}{9}\)%.

Take the cost prices as ₹ 400 and ₹ 500 (ratio 4 : 5) and apply each profit:

\[ \begin{aligned} SP &= 440 + 600 = 1040 \\ CP &= 400 + 500 = 900 \\ \text{Profit \%} &= \frac{140}{900} \times 100 \\ &= 15\tfrac{5}{9}\% \end{aligned} \]

The trap is to average the two rates to 15%, which ignores that the second bag cost more and so carries more weight. The other fractional options do not come from any correct weighting of 10% and 20% in the ratio 4 : 5.

Answer: C

The gain is 10%.

Let the cost price of one article be Rs. 1. Then the selling price of 10 articles equals the cost of 11 articles, Rs. 11.

\[ \begin{aligned} \text{gain} &= 11 - 10 = 1 \\ \text{gain\%} &= \frac{1}{10} \times 100 = 10\% \end{aligned} \]

The gain is reckoned on the cost price of the 10 articles sold, Rs. 10. Dividing by 11 instead gives about 9.1%, which is not offered.

A shortcut for such questions: when the selling price of x articles equals the cost price of y articles, the gain per cent is (y − x)/x × 100.

Answer: B

Sounak bought the fan 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 other prices do not give an 8% gain: from Rs. 748 the gain would be about 8.3%, from Rs. 760 about 6.6% and from Rs. 770 about 5.2%.

Answer: C

Total cost to produced \(1500\) watches \(= (1500 \times 150 + 30000) = Rs. 2,55,000\)

Let he sells \(x\) watches during the season, therefore

Number of watches sold after the season \(= (1500 - x)\)

\(\Rightarrow 250 \times x + (1500 - x) \times 100 = 150x + 150000\)

Now, break - even is achieved if production cost is equal to the selling price.

\(150x + 150000 = 2,55,000\)

\(x = 700\)

Answer: B

Cost Price of \(1st\) transistor \(= Rs. (\frac{100}{120} \times 840) = Rs. 700.\)

Cost Price of \(2nd\) transistor \(= Rs. (\frac{100}{96} \times 960) = Rs. 1000\)

So, total Cost Price \(= Rs. (700 + 1000) = Rs. 1700.\)

Total Selling Price \(= Rs. (840 +960) = Rs. 1800.\)

\(\therefore\) Gain % \(= (\frac{100}{1700} \times 100)\) % \(= 5\frac{15}{17}\) %