Question

A shopkeeper makes a profit of 17% by giving a discount of 22% on the marked price of an article. But with a view to gain more profit, he reduces the discount to 18% and makes a higher profit. How much is the difference in his profit percentage with this reduction in discount?

• A. 6%
• B. 7.5%
• C. 8%
• D. 9%

Hint:

Always take the marked price as \rupee100 to simplify problems involving discount and profit. Then calculate the selling price and compare with cost price to find profit%.

Answer 1

The Correct Option is A

Step 1: Assume the Marked Price (M.P.) = \rupee100.
When discount is 22%, Selling Price (S.P.) = \( 100 - 22\) = \rupee78 Let Cost Price (C.P.) be \( x \). Given profit = 17%: \[ \frac{78 - x}{x} \times 100 = 17 \quad \Rightarrow \quad \frac{78 - x}{x} = \frac{17}{100} \] \[ \Rightarrow 100(78 - x) = 17x \quad \Rightarrow \quad 7800 - 100x = 17x \] \[ \Rightarrow 7800 = 117x \quad \Rightarrow \quad x = \frac{7800}{117} = \rupee66.67 \] Step 2: When discount is 18%, new S.P. = \rupee82 \[ \text{New profit%} = \frac{82 - 66.67}{66.67} \times 100 \approx \frac{15.33}{66.67} \times 100 \approx 23% \] Step 3: Difference in profit percentage = \( 23% - 17% = \boxed{6%} \)