Question

A man purchases two clocks A and B at a total cost of $₹650$. He sells A at $20\%$ profit and B at a loss of $25\%$ and gets the same selling price for both the clocks. What are the purchasing prices of A and B respectively?

Answer 1

Let the cost price of clock A be $₹x$ and that of clock B be $₹(650-x)$.

From the given information, we can write

$120\%$ of $x=75\%$ of $(650-x)$

Therefore,

$$\begin{gathered} \frac{120}{100}\times x=\frac{75}{100}\times (650-x) \\ \Rightarrow x=\frac{75}{120}\times (650-x) \\ \Rightarrow x=\frac{5}{8}\times (650-x) \\ \Rightarrow 8x=3250-5x \\ \Rightarrow 8x+5x=3250 \\ \Rightarrow 13x=3250 \\ \Rightarrow x=\frac{3250}{13} \\ \Rightarrow x=250 \end{gathered}$$

Hence, the cost of clock A$\mathbf{}\mathbf{=}\mathbf{}\mathbf{₹}\mathbf{}\mathbf{250}$

So, the cost of clock B $=₹(650–250)=\mathbf{₹}\mathbf{}\mathbf{400}$

Hence, the purchasing price of clock A is $\mathbf{₹}\mathbf{}\mathbf{250}$ and clock B is $\mathbf{₹}\mathbf{}\mathbf{400}$.