Question

A shopkeeper sells a T.V. set of $\text{Rs}16560$ at $10\%$ discount on its marked price and earns $15\%$ profit. If no discount is offered, then what will be his present profit?

• A. $33\frac{1}{3}\%$
• B. $\frac{250}{9}\%$
• C. $\frac{27}{9}\%$
• D. $\frac{500}{9}\%$

Answer 1

The correct option is B $\frac{250}{9}\%$

Cost price of the article$=\text{Rs}16560$

let marked price be $\text{Rs}x$

discount $=10\%$

$\text{S.P.=M.P.}\left(\frac{100-\text{discount \%}}{100}\right)$

$=x\left(\frac{100-10}{100}\right)$

$=\frac{9x}{10}$

Profit $=15\%$

Profit $\%=\frac{\text{Profit}}{C.P.}\times 100$ Where, Profit $=$ Selling price $-$ Cost price

$⟹15=\frac{S.P.-C.P.}{C.P.}\times 100$

$⟹15\times 16560=(\frac{9x}{10}-16560)\times 100$

$⟹15\times 1656=9x-165600$

$⟹9x=165600+24840=190440$

$⟹x=21160$

$\therefore M.P.=21160$

If no discount is offered then $S.P.=M.P.$

$\therefore Profit=S.P.-C.P.$

$=21160-16560$

$=4600$

$\therefore Profit\%=\frac{Profit}{C.P.}\times 100$

$=\frac{4600}{16560}\times 100\%$

$=\frac{250}{9}\%$

$\therefore$ Profit is $\frac{250}{9}\%$