Question

Neha sold her old bicycle suffering a loss of $6\%$. If she had sold her bicycle for Rs. $90$ more, she would have made a profit of $3\%$. Find the cost price of the bicycle.

Answer 1

Let C.P. be $x$ and Orignal S.P. be $y$

$\Rightarrow$ loss% =$\frac{C.P.-S.P.}{C.P.}\times 100$

$6\%$ loss

$\Rightarrow \frac{6}{100}=\frac{x-y}{x}\Rightarrow \frac{y}{x}=\frac{94}{100}\Rightarrow y=\frac{94x}{100}$ and

$3\%$ loss

$\frac{3}{100}=\frac{(y+90)-x}{x}\Rightarrow 3x=100y+9000-100x$

$\Rightarrow 103x=100\left(\frac{94x}{100}\right)+9000$

$\Rightarrow 9x=9000\Rightarrow x=Rs.1000$

The cost price of the bicycle is Rs. $1000$.