Question

$P$ sold an article to $Q$ at $20\%$ profit. $Q$ sold it to $R$ at $25\%$ profit. If the difference in the cost prices of $Q$ and $R$ is $rs90$, find the cost price of the article for $P$.

• A. $Rs270$
• B. $Rs360$
• C. $Rs300$
• D. $Rs250$

Answer 1

Answer: (C)

$Rs300$

$P\underrightarrow{20\%profit}Q\underrightarrow{25\%profit}$

let $C.P$ of $P$ be $Rsx$

$\therefore$ profit of $P=Rs\frac{20x}{100}S.P=Rs(x+\frac{20x}{100})=Rs\frac{120x}{100}$

$S.P.$ of $P=C.P$ of $Q.$

Profit of $Q=Rs(\frac{120x}{100}\times \frac{25}{100})=Rs\frac{30x}{100}$

$\therefore S.P=Rs(\frac{120x}{100}+\frac{30x}{100})=Rs\frac{150x}{100}$

$S.P$ of $Q=C.P$ of $R$.

Now , $C.P$ of $Q-C.P$ of $R=-Rs90$

Or, $\frac{120x}{100}-\frac{150x}{100}=-90$

Or , $-\frac{30x}{100}=-90\Rightarrow x=300$

$\therefore C.P$ of $P=Rs300$