Question

A man sold an article for 495 and gained 10% on it. Find the cost price of the article.

Answer 1

$$\begin{gathered} \begin{array}{l}\text{Let the cost price of the article be Rs}x.\\ \text{According to the question, we have:}\\ \text{SP}=\mathrm{Rs}\text{495}\end{array} \\ \therefore \text{Gain \%=}\frac{\text{Gain}}{\mathrm{CP}}\text{×100} \\ \Rightarrow 10=\frac{\mathrm{Gain}}{x}\times 100 \\ \Rightarrow \mathrm{Gain}=\frac{10x}{100}=\mathrm{Rs}\frac{x}{10} \\ \begin{array}{l}\text{Now, CP}+\mathrm{Gain}=\text{SP}\\ \Rightarrow x+\frac{x}{10}=495\\ \Rightarrow \frac{x+10x}{10}=495\\ \Rightarrow 11x=495\times 10\\ \Rightarrow x=\frac{495\times 10}{11}\\ \Rightarrow x=\frac{4950}{11}\\ \Rightarrow x=450\\ \therefore \text{CP}=\text{Rs 45}0\end{array} \end{gathered}$$