(solved)Question 8 SSC-CGL 2020 March 4 Shift 1

Question 8
SSC-CGL 2020 Mar 4 Shift 1

A shopkeeper gives two successive discounts of 25% and 20% respectively and still earns 20% profit. If no discount was given by the shopkeeper, then the profit% would have been?

Solution in Detail

Let CP = $\displaystyle 100$

After discounts profit is $\displaystyle 20\%$

$\displaystyle \therefore$ SP = $\displaystyle 100 + 20\% = 120$

Let MP = x

There are two successive discounts

$\displaystyle 25\% \equiv \frac 14, 20\%\equiv \frac 15$

SP after these discounts

$\displaystyle 120 = x (1 - 1/4) ( 1 - 1/5)$

$\displaystyle \therefore x = 200$

We have to calculate his profit if he had sold at this marked price, i.e., without giving any discounts. So take his $\displaystyle SP$ as $\displaystyle = MP = 200$

Profit $\displaystyle = \frac{SP - CP}{CP} \times 100$

$\displaystyle = \frac{200 - 100}{100} \times 100 $

$\displaystyle = 100\%\:\underline {Ans}$