Question : If the selling price of 9 boxes is equal to the cost price of 15 boxes. The gain percentage is (The selling price of all boxes is the same and the cost price of all boxes is the same):
Option 1: $\frac{50}{3}\%$
Option 2: $\frac{200}{3}\%$
Option 3: $\frac{100}{3}\%$
Option 4: $\frac{140}{3}\%$
Correct Answer: $\frac{200}{3}\%$
Solution :
Let the cost price of one box as C and the selling price of one box as S.
Given that the selling price of 9 boxes is equal to the cost price of 15 boxes.
⇒ 9S = 15C
⇒ S = $\frac{15}{9}$C = $\frac{5}{3}$C
This means the selling price is $\frac{5}{3}$ times the cost price.
Profit = Selling price – Cost price = $\frac{5}{3}$C – C = $\frac{2}{3}$C
Profit percentage = $\frac{\text{Profit}}{\text{Cost price}}$ × 100
= $\frac{\text{2}}{\text{3}}$ × 100
= $\frac{\text{200}}{\text{3}}\%$
Hence, the correct answer is $\frac{\text{200}}{\text{3}}\%$.
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