Question

A fruit-seller sells $4$ oranges for Rs. $3$, gaining $50\%$. After giving successive discounts of 10% and 20% he gains $50\%$ profit. Calculate the equivalent discount.

Answer 1

Say the Marked Price (M.P) be Rs. 100, and given $d_1$ = 10% and $d_2$ = 20% then

S.P =$\left(\frac{100-d_1}{100}\right)\times \left(\frac{100-d_2}{100}\right)\times .M.P$

S.P =$\left(\frac{100-10}{100}\right)\times \left(\frac{100-20}{100}\right)\times 100$

S.P =$\left(\frac{90}{100}\right)\times \left(\frac{80}{100}\right)\times 100$

S.P =$\left(\frac{72}{100}\right)\times 100$

S.P $=$ Rs. $72$

The single equivalent discount = M.P - S.P = Rs. 100 - Rs. 72 = Rs. 28

$\therefore$ Single equivalent discount %

$=$ $\frac{\text{Single Equivalent Discount}}{M.P}$

$=28/100=28\%$

Ans $=28\%$