Question

A shop-keeper purchases $11$ knives in Rs. $10$ and sells them at the rate of $10$ knives for Rs.$11$. He earns a profit of

• A. $11$ $\%$
• B. $15$ $\%$
• C. $17$ $\%$
• D. $21$ $\%$

Answer 1

The correct option is D $21$ $\%$

C.P. of $1$ knife $=\frac{10}{11}$
S.P of $1$ knife $=\frac{11}{10}$
Profit $=$ S.P $-$ C.P
Profit =$\frac{11}{10}-\frac{10}{11}=\frac{121-100}{110}=\frac{21}{110}$

Profit $\%$ $=\frac{\text{profit}}{\text{C.P.}}\times 100$

Profit $\%$ $=\frac{\frac{21}{110}}{\frac{10}{11}}\times 100$

$\Rightarrow \frac{21}{110}\times \frac{11}{10}\times 100=21$ $\%$