Question

By selling $33$ m of carpet, a man loses an amount equal to the selling price of $3$ m of carpet. Find his gain or loss per cent.

• A. $8\frac{1}{3}\%$
  
• B. $8\%$
• C. $8\frac{1}{2}\%$
• D. $8\frac{2}{3}\%$
• E. Cannot be determined

Answer 1

The correct option is A $8\frac{1}{3}\%$

Loss $=($C.P. of $33)$ m $-($ S.P. of $33)$ m

$\Rightarrow ($ S.P. of $3)$m $=($ C.P. of $33)$ m$-($ S.P. of $33)$ m

$\Rightarrow ($ S.P. of $33)$ m $+($ S.P. of $3)$ m $=($ C.P. of $33)$ m

$\Rightarrow ($ S.P. of $36)$ m $=($ C. P. of $33)$ m

Let C. P. of $1$ m $=x$

Then, C.P. $36$ m $=36x$

S.P of $36$ m $=($ C.P. of $33)$ m $=33x$

Thus, C.P. $=36x$ and S.P . $=33x$

Since, C.P. $>$ S.P., there is a loss.

Loss $=(36x-33x=3x)$

Loss $\%=[\left(\frac{loss}{C.P.}\right)\times 100]\%$

$=[\left(\frac{3x}{36x}\right)\times 100]\%$

$=\frac{25}{3}\%$

$=8\frac{1}{3}\%$