Question

A retailer purchases shirts from a distributor at the rate of 300 per shirt and puts the label of 450 on each shirt. If the retailer allows some discount and still make a profit of 23%, then what is the discount percentage offered by the shopkeeper?

• A. 16%
• B. 17%
• C. 18%
• D. 19%

Answer 1

The Correct Option is C

Finding the Discount Percentage

Step 1: Given Data 

• Cost Price (C.P.) = Rs. 300
• Marked Price (M.P.) = Rs. 450
• Profit Percentage = 23%

Step 2: Calculate the Selling Price (S.P.)

The selling price is given by:

\[ S.P. = C.P. \times \left(1 + \frac{23}{100} \right) \]

Substituting the values:

\[ S.P. = 300 \times 1.23 = 369 \]

Step 3: Compute the Discount Percentage

The shopkeeper offers a discount on the marked price, so:

\[ S.P. = M.P. \times \left(1 - \frac{x}{100} \right) \]

Substituting the values:

\[ 450 \times \left(1 - \frac{x}{100} \right) = 369 \]

Step 4: Solve for \( x \)

Dividing both sides by 450:

\[ 1 - \frac{x}{100} = \frac{369}{450} \]

\[ 1 - \frac{x}{100} = 0.82 \]

Solving for \( x \):

\[ \frac{x}{100} = 1 - 0.82 = 0.18 \]

\[ x = 18 \]

Final Answer:

Thus, the discount percentage is 18% (Option C).