Question

A person sells an article for Rs.75 and gains as much per cent as the cost price of the article. What is the cost price of the article ?

• A. Rs. 40
• B. Rs. 50
• C. Rs. 60
• D. Rs. 75

Answer 1

Answer: (B)

Rs. 50

Let the C.P. of the article be Rs.$x$

Then Gain $=x\%$
$\therefore$ S.P. $=\frac{(100+x)\times }{100}=\frac{100x+x^2}{100}$ Given $\frac{x^2+100x}{100}=75\Rightarrow x^2+100x-7500=0$
$\Rightarrow x^2+150x-50x-7500=0\Rightarrow x(x+150)-50(x+150)=0$
$\Rightarrow (x-50)(x+150)=0\Rightarrow x=50or-150$
Neglecting negative value, $x=50$.