A shopkeeper fixes the marked price of an item 52% above its cost price. What percentage of discount on the marked price should be allowed to gain 14%?​

Correct option is D

Given:

The marked price is 52% above the cost price. The shopkeeper wants to gain a 14% profit.

Formula Used:

Profit = (Selling Price - Cost Price) / Cost Price * 100
Selling Price = Marked Price - Discount

Solution:
Let the cost price be C.
Then, the marked price is 52% more than the cost price: M = C + 0.52C = 1.52C.
The shopkeeper wants to gain a 14% profit, so:
Selling Price = C + 0.14C = 1.14C.
We know the selling price is the marked price minus the discount (D):
1.14C = 1.52C - D
Solving for D:
D = 1.52C - 1.14C = 0.38C.
Now, the percentage discount on the marked price is:
Discount Percentage = ($$\frac{D }{M}) \times 100 = (\frac{0.38C }{ 1.52C}) \times 100 = 25 \%$$​​
The percentage of discount on the marked price should be 25%.