Question

A shopkeeper sells a pair of sunglasses at a profit of $25\%$. If he had bought it at $25\%$ less and sold it for Rs. $10$ less then be would have gained $40\%$. The cost price of the pair of sunglasses is

• A. Rs. $25$
• B. Rs. $50$
• C. Rs. $60$
• D. Rs. $70$

Answer 1

The correct option is B Rs. $50$

Let the C.P. of the pair of sunglasses be Rs. $x$.

Then S.P. $=\frac{x\times 125}{100}=$ Rs. $\frac{5x}{4}$
New C.P. $=$ Rs.$(\frac{75}{100}\times x)=$ Rs. $\frac{3x}{4}$
New S.P. $=$ Rs.$(\frac{5x}{4}-10)$
Given, $\frac{5x}{4}-10=\frac{140}{100}\times \frac{3x}{4}$

$\Rightarrow \frac{5x}{4}-\frac{21x}{20}=10$
$\Rightarrow \frac{25x-21x}{20}=10$

$\Rightarrow 4x=200$

$\Rightarrow x=$ Rs. $50$