Question

A merchant gained a net gain of 18.75% on his cost of Rs. 20,000 after giving the agent a commission at 5% on the sale price. Find the sale price.

• A. Rs. $20,000$
• B. Rs. $30,000$
• C. Rs. $25,000$
• D. Rs. $18,000$

Answer 1

The correct option is C Rs. $25,000$

$\Rightarrow$ Let $x$ be the sale price

$\Rightarrow$ Commission = 5 % on sale=$\frac{5}{100}x=0.05x$

$\Rightarrow$ Gross Profit = Sale Price - Cost Price

$\Rightarrow$ Gross Profit $=x-20,000$

$\Rightarrow$ $NetProfit=GrossProfit-Commission$

$\Rightarrow$ Net Profit $=(x-20,000)-0.05x$

$\Rightarrow$ Net Profit $=0.95x-20,000$

$\Rightarrow$ But $NetProfit=18.75$

$\Rightarrow$ Net Profit $=\frac{18.75}{100}\times 20,000$

$\Rightarrow$ $NetProfit=Rs.3,750$

$\therefore$ $0.95x-20,000=3,750$

$\therefore$ $0.95x=23,750$

$\Rightarrow$ $x=\frac{23,750}{0.95}=25,000$

$\therefore$ The sale price is $Rs.25,000$