Question

A dealer allows a discount of $10\%$ and still gains $5\%.$ What percent above the cost price must he mark his goods?

• A. $15\%$
• B. $20\%$
• C. $16\frac{1}{3}\%$
• D. $50\%$

Answer 1

The correct option is C $16\frac{1}{3}\%$

Let $C.P.=\text{Rs}100$

$\because \left(\frac{S.P.-C.P.}{C.P.}\right)\times 100=\text{Profit}\%$

$⟹\left(\frac{S.P.-100}{100}\right)\times 100=5$

$⟹S.P.=\text{Rs}105$
Discount(d) $=10\%$

We have,
$S.P.=\frac{M.P.(100-d)}{100}$ (where $d,$ is discount)

$M.P.=\frac{105\times 100}{100-10}=\frac{105\times 100}{90}=\frac{350}{3}$

$M.P.-C.P.=\frac{350}{3}-100=\frac{50}{3}$

$\therefore \text{Required}\%=\frac{\frac{50}{3}}{100}\times 100=16\frac{2}{3}\%$

$\therefore$ He should mark his goods $16\frac{2}{3}\%$ above the C.P.