Question

Mohit sold a watch to Karim at a gain of $10\%$ and Karim sold it to Rahim at a gain of $4\%$. If Rahim pays $Rs.14300$ for it, for how much did Mohit purchase it?

Answer 1

Let, Mohit sold a watch to Karim at $Rs.x$
Mohit sold it at a gain of $10\%$.
SP of the watch for Mohit $=110\%$ of $x$ $=\frac{110x}{100}$$=\frac{11x}{10}$

Karim sold it to Rahim at a gain of $4\%$.
SP of the watch for Karim $104\%$ of $\frac{11x}{10}=\frac{104}{100}\times \frac{11x}{10}$
But, Rahim pays $Rs.14300$

$\Rightarrow \frac{104}{100}\times \frac{11x}{10}=14300$

$\Rightarrow 104\times 11x=14300\times 100\times 10$

$\Rightarrow x=\frac{14300\times 100\times 10}{104\times 11}$

$\Rightarrow x=12500$
Hence, Mohit purchased the watch at $Rs.12,500$.