Question

An article is sold at $10\%$ profit . If its cost price and selling price are $50$ less, the profit would be $5\%$ more. Find the cost price?

• A. $40$
• B. $45$
• C. $60$
• D. $120$
• E. $150$

Answer 1

Answer: (E)

$150$

$let,C.P=x$
and $gain\%=10\%$
$S.P=\left(\frac{100+gain}{100}\right)\times C.P\Rightarrow S.P=\frac{110x}{100}$
$newC.P=C.P-50$
$newS.P=S.P-50$
$gain\%=5\%morethanprevious=15\%$
$\Rightarrow NewS.P=\left(\frac{100+gain}{100}\right)\times (NewC.P)$
$\Rightarrow (S.P-50)=\left(\frac{100+15}{100}\right)\times (C.P-50)$
$\Rightarrow (\frac{110x}{100}-50)=\frac{115}{100}\times (x-50)$
$\Rightarrow \frac{110x}{100}-50=\frac{115x}{100}-\frac{115}{2}$
$\Rightarrow \frac{115}{2}-\frac{100}{2}=\frac{115x}{100}-\frac{110x}{100}$
$\Rightarrow \frac{15}{2}=\frac{5x}{100}$
$\therefore x=150$