Question

If the selling price of an article is $1\frac{1}{3}$ of it cost price, find the gain per cent.

Answer 1

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

$\Rightarrow$ S.P. of the article $=1\frac{1}{3}x=\frac{4x}{3}$

Since, $\frac{4x}{3}>x$

i.e., S.P $>$ C.P, will get gain.

$\Rightarrow$ Gain $=$ S.P $-$ C.P

$\Rightarrow$ Gain $=\frac{4x}{3}-x$

$\Rightarrow$ Gain $=\frac{4x-3x}{3}=\frac{x}{3}$---(1)

Gain percent $=\frac{\text{Gain}}{\text{C.P}}\times 100\%$

$=\frac{\frac{x}{3}}{x}\times 100\%$

$=\frac{1}{3}\times 100\%$

$=33\frac{1}{3}\%$

Hence, Gain is $33\frac{1}{3}\%$.