Question

A man sells an article at a gain of $20\%$. If he had bought it for $20\%$ less and sold it for $264$ less, he would have still gain $20\%$.The cost price of the article is ?

• A. Rs. $1100$
• B. Rs. $2400$
• C. Rs. $2600$
• D. Rs. $2650$

Answer 1

The correct option is A Rs. $1100$

Let C.P. be $X$

Hence, S.P. $=X+20\%$ of $X=X+\frac{20}{100}\times X=1.2X$
If he had bought it for $20\%$ less

Then, new C.P. $=X-20\%$ of $X=X-\frac{20}{100}X=0.8X$
And new S.P. $=1.2X-264$

Gain $=20\%$
$\Rightarrow \frac{(1.2X-264)-.8X}{.8X}=\frac{20}{100}$

$\Rightarrow \frac{.4X-264}{.8X}=\frac{20}{100}$

$\Rightarrow 40x-26400=16x$

$\Rightarrow 24x=26400$

$\Rightarrow X=1100$
Thus, C.P. of the article $=$ Rs. $1100$.