Question

A cycle was sold at a gain of 10%. Had it been sold for Rs 65 more, the gain would have been 14%. Find the cost price of the cycle.

Answer 1

Let the cost price of the cycle be Rs x.
$$\begin{gathered} \mathrm{SP}ofthecycleat10\%gain=\mathrm{Rs}\left\{\frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP}\right\} \\ =\mathrm{Rs}\left\{\frac{100+10}{100}\times x\right\} \\ =\mathrm{Rs}\left\{{\displaystyle \frac{110x}{100}}\right\} \\ =\mathrm{Rs}.\frac{11x}{10} \end{gathered}$$

$$\begin{gathered} \mathrm{SP}\mathrm{of}\mathrm{the}\mathrm{cycle}\mathrm{at}\mathrm{14\%}gain=\mathrm{Rs}\left\{\frac{100+14}{100}\times x\right\} \\ =\mathrm{Rs}\left\{{\displaystyle \frac{114x}{100}}\right\} \\ =\mathrm{Rs}\left\{\frac{57x}{50}\right\} \\ \therefore \frac{57x}{50}-\frac{11x}{10}=65 \\ \Rightarrow \left(\frac{57x}{50}-\frac{55x}{50}\right)=65 \\ \Rightarrow \frac{57x-55x}{50}=65 \end{gathered}$$
$$\begin{gathered} \Rightarrow \frac{2x}{50}=65 \\ \Rightarrow 2x=3250 \\ \Rightarrow x=1625 \end{gathered}$$

Therefore, the cost price of the cycle is Rs 1625.