Question

A man purchased some eggs at 3 for ₹ 16 and sold them at 5 for ₹ 36. Thus, he gained ₹ 168 in all. How many eggs did he purchase?

Answer 1

Let the number of eggs purchased be x.
CP of 3 eggs = ₹16
∴ CP of 1 egg = $₹\frac{16}{3}$
⇒ CP of x eggs = $₹\frac{16}{3}x$
SP of 5 eggs = ₹36
∴ SP of 1 egg = $₹\frac{36}{5}$
⇒ SP of x eggs = $₹\frac{36}{5}x$
Gain = SP − CP = ₹168
$$\begin{gathered} \therefore \frac{36}{5}x-\frac{16}{3}x=168 \\ \Rightarrow \frac{28}{15}x=168 \\ \Rightarrow x=\frac{168\times 15}{28} \\ \Rightarrow x=90 \end{gathered}$$
Hence, the man purchased 90 eggs.