Question

If an article is sold at $8\%$ profit instead of $8\%$ loss, it would have brought Rs. $12$ more, what is the cost price of the article?

• A. Rs. $60$
• B. Rs. $70$
• C. Rs. $72$
• D. Rs. $75$

Answer 1

Answer: (D)

Rs. $75$

Let the Cost Price (C.P) be Rs $x$ and then at $8\%$ of profit

Selling Price(S.P) would be :

Gain $\%$ = $\frac{(S.P-C.P)}{C.P}\times 100$

$\Rightarrow 8\%=\frac{S.P-x}{x}\times 100$

$\Rightarrow \frac{8x}{100}=S.P-x$

$\Rightarrow S.P=\frac{8x}{100}+x$

$\Rightarrow S.P=\frac{108x}{100}$ .....(1)

Now, If the loss is $8\%$

$\Rightarrow \frac{8x}{100}=x-S.P$

$\Rightarrow S.P=\frac{92x}{100}$...(2)

Now we have the condition from 1 and 2 we get :

$S.P\left(profit\right)=S.P\left(loss\right)+12$

$\Rightarrow \frac{108x}{100}=\frac{92x}{100}+12$

$\Rightarrow \frac{(108-92)}{100}x=12$

$\Rightarrow \frac{16}{100}x=12$

$\Rightarrow 16x=12\times 100$

$\Rightarrow x=\frac{12\times 100}{16}$

$\Rightarrow x=75$

$\Rightarrow C.P=$Rs $75$

The Cost Price of the article is $Rs75$ .