Question

A trader bought an article for Rs. $x$ and sold it for Rs. $52$, thereby making a profit of $(x-10)$ per cent on his outlay. Calculate the cost price.

• A. Rs. $60$
• B. Rs. $70$
• C. Rs. $80$
• D. Rs. $40$

Answer 1

Answer: (D)

Rs. $40$

Let the cost price of the article be $x$.

Its is given that selling price is Rs.$52$ and profit is $(x-10)$ percent.

Therefore,

$\frac{SP-CP}{CP}\times 100=(x-10)\Rightarrow \frac{52-x}{x}\times 100=(x-10)\Rightarrow 100(52-x)=x(x-10)\Rightarrow 5200-100x=x^2-10x\Rightarrow x^2-10x+100x-5200=0\Rightarrow x^2+90x-5200=0\Rightarrow (x-40)(x+130)=0\Rightarrow x-40=0,x+130=0\Rightarrow x=40,x=-130$

Negative value is neglected and therefore, $x=40$.

Hence, the cost price of the article is Rs.$40$.