Question

A man sells a book at a profit of $25\%$. If he had bought it at $20\%$ less and sold it for Rs. $10.50$ less, he would have gained $30\%$. The cost price of the book is

• A. Rs. $50$
• B. Rs. $20$
• C. Rs. $25$
• D. Rs. $35$

Answer 1

The correct option is A Rs. $50$

Let C.P.be $100$.

Gain $=25\%$

S.P. $=100+25\%$ of $100=125$

Suppose C.P. $=80$

Gain $=30\%$

S.P. $=\frac{130\times 80}{100}=104$

Difference $=125-104=21$

Now comparing difference

A difference of $\text{Rs.}21$ is obtained on C.P. =$\text{Rs.}100$

A difference of $\text{Rs.}1$ is obtained on C.P. = $\text{Rs.}\frac{100}{21}$

A difference of $\text{Rs.}10.50$ will be obtained on C.P. $=\text{Rs.}10.50\times \frac{100}{21}=\text{Rs.}50$

So, required C.P. $=\text{Rs.}50$.