Question

If the selling price of a mat is five times the discount offered and if the percentage of discount is equal to the percentage profit, find the ratio of the discount offered to the cost price.

Answer 1

Since $SP=5\times$ discount offered

$\Rightarrow S.P=5(MP-SP)$

$\Rightarrow S.P=5M.P-5S.P$

$\Rightarrow 6S.P=5M.P$

$\Rightarrow M.P=\frac{6}{5}S.P$

Since the percentage discount = percentage profit

$\frac{\frac{6}{5}S.P-S.P}{\frac{6}{5}S.P}\times 100=\frac{S.P-C.P}{C.P}\times 100$

$\Rightarrow \frac{S.P}{S.P}\left(\frac{6-5}{\frac{5}{615}}\right)\times 100=\frac{S.P-C.P}{C.P}\times 100$

$\Rightarrow \frac{1}{6}=\frac{S.P}{C.P}-1\Rightarrow \frac{S.P}{C.P}=\frac{1}{6}+1=\frac{7}{6}$

$M.P=\frac{6}{5}S.P=\frac{6}{5}\times \frac{7}{6}CP=\frac{7}{5}C.P$

$\therefore$ Ratio of discount to C.P

$=\frac{M.P-S.P}{C.P}$

$=\left[\frac{\frac{7}{5}C.P-\frac{7}{5}CP}{C.P}\right]=\frac{7}{5}-\frac{7}{6}$

$=7(\frac{1}{5}-\frac{1}{6})$

$=7\left(\frac{6-1}{30}\right)$

$=\frac{7}{30}$

$\therefore$ Ratio is 7:30