A shopkeeper sells an item at 20% discount on the marked…

A shopkeeper sells an item at 20% discount on the marked price and earns a profit of 90%. If he sells the same item at 40% discount, then his new profit percentage will be:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 42.5%.

Given that, discount, D = 20%

Profit, P = 90%

SP = MP × ${100 - D}\over 100$

SP = CP × ${100 + P}\over 100$

Let the MP of the item be 100x.

According to the given question,

SP = 100x × ${100 - 20}\over 100$

⇒ SP = 80x

Now, 80x = CP × ${100 + 90}\over 100$

⇒ CP = 42.105x

New discount = 40%

SP = 100x × ${100 - 40}\over 100$

⇒ SP = 60x

Profit = SP - CP

⇒ 60x - 42.105x = 17.895x

Profit percentage = ${17.895x \over 42.105x} \times 100$ = 42.5%

SSC CHSL 2024 PYQ — Question 52