Question

A person sells 36 oranges per rupee and incurs a loss of $4\%$. Find how many oranges are to be sold for a rupee to have a gain of $8\%$?

• A. 32
• B. 30
• C. 28
• D. 34

Answer 1

The correct option is A

32

If a person sells 36 oranges for 1 rupee, then the selling price is Rs. $\frac{1}{36}$.

Let the cost price of one orange be Rs. x.

Given, $\frac{x-\frac{1}{36}}{x}=\frac{4}{100}$

$\Rightarrow 100\times (x-\frac{1}{36})=4x$

$\Rightarrow 100x-\frac{100}{36}=4x$

$\Rightarrow 96x=\frac{100}{36}$

$\Rightarrow x=\frac{100}{36\times 96}=\frac{25}{864}$

Let the required selling price be Rs. y, for which the profit is 8%.

$\Rightarrow \frac{y-\frac{25}{864}}{\frac{25}{864}}=\frac{8}{100}$

$\Rightarrow y-\frac{25}{864}=\frac{8}{100}\times \frac{25}{864}$

$\Rightarrow y-\frac{25}{864}=\frac{2}{864}$

$\Rightarrow y=\frac{27}{864}=\frac{1}{32}$

Thus, to get a profit of 8%, the selling price of an orange should be Rs. $\frac{1}{32}$

Or, for 1 rupee, 32 oranges must be sold.