Question

A man bought a chair and sold it at a gain of $5$%. If he had bought it at $5$% less and sold it for Rs $45$ more, he would have gained $20$% . Find the cost price of the chair?

• A. Rs. $400$
• B. Rs. $500$
• C. Rs. $450$
• D. Rs. $550$

Answer 1

The correct option is B Rs. $500$

Let CP = x
$SP=x+5\%ofx=x+\frac{5x}{100}=\frac{105x}{100}=1.05x$
Now,
If he had bought it in 5% less,
$CP=x-5\%ofx=x-\frac{5x}{100}=\frac{95x}{100}=0.95x$
New SP$=1.05x+45$
New gain$=20\%of0.95x$

$S.P-C.P=gain$
$\Rightarrow 1.05+45-0.95x=\frac{20}{100}\times 0.95x$
$\Rightarrow 0.1x+45=0.19x$
$\Rightarrow 0.09x=45$
$\Rightarrow x=500$
CP = Rs. 500