Question

A sold an article to $B$ at a loss of $10\%$. Had he sold it for $Rs.108$ more, he would have gained $8\%$. Find the $C.P.$ for $A$

• A. Rs. $550$
• B. Rs. $600$
• C. Rs. $2000$
• D. None of these

Answer 1

Answer: (B)

Rs. $600$

Let Cost Price of article for $A$ be $x$ and Selling price

Case (1) $loss=C.P-S.P$

$\Rightarrow \frac{10}{100}C.P=$ $C.P-S.P$

$\Rightarrow \frac{x}{10}=x-y$

$\Rightarrow y=x-\frac{x}{10}=\frac{9x}{10}$

$\Rightarrow y=\frac{9x}{10}$ ..... $\left(1\right)$

Case (2) If $S.P=y+108$ then gain $=8\%$

gain $=S.P-C.P$

$\Rightarrow \frac{8}{100}x=$ $y+108-x$

$\Rightarrow \frac{8}{100}x+x=y+108$

$\Rightarrow \frac{27x}{25}=y+108$

$\Rightarrow \frac{27x}{25}=y+108$

$\Rightarrow \frac{27}{25}x=\frac{9x}{10}+108$ ....... from $\left(1\right)$

$\Rightarrow \frac{27}{25}x-\frac{9x}{10}=108$

$\Rightarrow \frac{(54-45)}{50}x=108$

$\Rightarrow \frac{9x}{50}=108$

$4x=600$ Rs

So, C.P of article for $B$ is Rs $600$