Question

A bicycle is sold at a gain of $16\%$. Had it been sold $Rs100$ more, the gain would have been $20\%$. Find the $C.P$ of the bicyle.

Answer 1

Let cost price $=C.PandSellingprice=S.P$

$\Rightarrow Gain$% $=\frac{S.P-C.P}{C.P}\times 100\Rightarrow \frac{16}{100}=\frac{S.P-C.P}{C.P}\Rightarrow \frac{SP}{CP}=\frac{116}{100}$

and $\frac{20}{100}=\frac{S.P+100-C.P}{C.P}\Rightarrow \frac{1}{5}=\frac{SP}{CP}+\frac{100}{CP}-1$

$\Rightarrow \frac{6}{5}=\frac{116}{100}+\frac{100}{CP}\to \frac{100}{C}=\frac{6}{5}-\frac{58}{50}=\frac{300-290}{250}=\frac{10}{250}$

$\Rightarrow CP=\frac{100\times 250}{10}=Rs.2500$