A shopkeeper sells an item by giving 25% discount on its marked price and still gains 35%. If the cost price of the item decreases by 10%, and he sells it by allowing 37.5% discount on the same marked price, then his gain percentage will be ____________.

Correct option is C

Given:
Marked Price = ₹100 (assumed for ease of calculation)
In the first case:
Discount = 25%
Gain = 35%
In the second case:
Cost price decreases by 10%
Discount = 37.5%
Find the new gain percentage.

Formula Used:

​$$\text{1. Selling Price (SP)} = \text{Marked Price} \times \left( \frac{100 - \text{Discount \%}}{100} \right) \\[8pt]\text{2. Gain \%} = \left( \frac{\text{SP} - \text{CP}}{\text{CP}} \right) \times 100 \\[8pt]\text{3. Reduced Cost Price} = \text{Original CP} \times \left( \frac{100 - \text{Reduction \%}}{100} \right)$$​​

Solution:

Let the Marked Price (MP) be ₹100.

Case 1:

• Discount = 25% → Selling Price (SP) = 75% of ₹100 = ₹75
• Gain = 35%, so:

Let Cost Price (CP) be ₹x.
Given:
SP = CP + 35% of CP = 1.35 × CP

So,
75 = 1.35 × CP
CP = 75 / 1.35 = ₹55.56 (approx)

Case 2:

• New CP = 10% less → New CP = 90% of ₹55.56 = ₹50
• New discount = 37.5% → SP = 62.5% of ₹100 = ₹62.5

Now,
Gain = SP − CP = ₹62.5 − ₹50 = ₹12.5
Gain % = (12.5 ÷ 50) × 100 = 25%

Final Answer: (C) 25%