Question

The marked price of a radio is Rs. 1200. The shopkeeper allows a discount of 12 percent and still gains 32 percent. If no discount is allowed, find his gain percent.
1. 20 percent
2. 47.84 percent
3. 44 percent
4. 50 percent

Answer 1

Correct Answer - Option 4 : 50 percent

Given:

The marked price of a radio is Rs. 1200.

The shopkeeper allows a discount of 12% 

Profit is 32%

Concept used:

CP/MP = (100 - D%)/(100 + P%)

P = SP - CP

P% = (P/CP) × 100

where, CP is Cost price, MP is Marked price, D% is Discount percent, P% is Profit percent and P is Profit

Calculations:

According to the question, we have

CP/MP = (100 - D%)/(100 + P%)

⇒ CP/1200 = (100 - 12)/(100 + 32)

⇒ CP = (88/132) × 1200

⇒ CP = (2/3) × 1200

⇒ CP = Rs. 800

If no discount is allowed, then SP is Rs. 1200 and the profit is 

P = SP - CP

⇒ P = Rs. 1200 - Rs. 800

⇒ P = Rs. 400

So, Profit percent is 

P% = (P/CP) × 100

⇒ P% = (400/800) × 100

⇒ P% = 50%

∴ The profit percentage is 50%.