Question : A dealer allows a 25% discount on the marked price of an article and gains 20%. If the cost price of the article increases by 20%, how much discount percentage should he allow on the marked price to earn the same percentage of profit as before?
Option 1: 12%
Option 2: 8.5%
Option 3: 10%
Option 4: 7.25%
Correct Answer: 10%
Solution :
Let the marked price be Rs.100
Selling price = 100× $\frac{75}{100}$ = Rs. 75
⇒120% of the cost price = 75
⇒ Cost price = 75 × $\frac{100}{120}$
New cost price = 120% of old cost price
New cost price = 100 × $\frac{75}{100}$ × $\frac{100}{120}$ = Rs.75
Since the profit percentage remains the same
⇒ New selling price = 75 × $\frac{100}{120}$ = Rs.90
New discount = $\frac{\text{100 - 90}}{\text{100}}$ × 100 = 10%
Hence, the correct answer is 10%.
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