# Difficult Percentages Solved QuestionAptitude Discussion

 Q. After offering a discount of $37.5%$, Pankaj sold the rice at a profit of $25%$. Had he offered a discount of $41.67%$, his profit or loss percent would have been:
 ✔ A. $16.66\%$  profit ✖ B. $12\%$ loss ✖ C. $29.17\%$ loss ✖ D. $8.33\%$ profit

Solution:
Option(A) is correct

Let the marked price of the rice = $8p$

Discount

$=37.5\%=\dfrac{3}{8}\times MP$

Selling price

$=8p-\dfrac{3}{8}\times 8p=5p$

$5p= CP +\dfrac{25}{100}\times 25$

$\Rightarrow CP =4p$

If he had offered a discount of $41.67\%=\dfrac{5}{12}$

$SP =8p-\dfrac{5}{12}\times 8p$

$=\dfrac{14p}{3}$

Profit

$=\dfrac{14p}{3}-4p$

$=\dfrac{2p}{3}$

Profit percentage

$=\dfrac{2p/3}{4p}\times 100$

$=\dfrac{100}{6}\%$

$=16.66\%$

Edit: For shortcut method please see Thulasi's comment.

## (4) Comment(s)

Vineet
()

A person gets 3 successive discounts of 28.56%, 12.5% and 60%. The net discount is?

.

Thulasi
()

let M.P $= 100$,

$100-37.5=62.5 =$ SP

$\dfrac{62.5}{5}\times 4=50=$ CP

Now $100-41.67=58.33=$ new SP

$\dfrac{8.33}{50} \times 100=16.67\%$

Raman
()

Wow that a cool short trick.

Ned Stark
()

wow good short cut