A shopkeeper marks his goods 20% more than the C.P. and allows a discount of 15%. Find the profit percentage of the shopkeeper.

Options

A. 0.02
B. 0.04
C. 0.01
D. 0.03

Answer

To find the profit percentage of the shopkeeper, let's break down the problem step by step.

### Step 1: Determine the Cost Price (C.P.)
Let’s assume the Cost Price (C.P.) of the goods is \(100\) (for simplicity).

### Step 2: Calculate the Marked Price (M.P.)
The shopkeeper marks his goods 20% more than the C.P.
- Marked Price (M.P.) = C.P. + 20% of C.P.
- M.P. = \(100 + 20\% \times 100\)
- M.P. = \(100 + 20 = 120\)

### Step 3: Calculate the Selling Price (S.P.)
The shopkeeper allows a discount of 15% on the M.P.
- Discount = 15% of M.P.
- Discount = \(15\% \times 120 = 18\)
- Selling Price (S.P.) = M.P. - Discount
- S.P. = \(120 - 18 = 102\)

### Step 4: Calculate the Profit
Profit is calculated as:
- Profit = Selling Price - Cost Price
- Profit = \(102 - 100 = 2\)

### Step 5: Calculate the Profit Percentage
Profit percentage is calculated using the formula:
- Profit Percentage = \(\frac{\text{Profit}}{\text{C.P.}} \times 100\)
- Profit Percentage = \(\frac{2}{100} \times 100 = 2\%\)

### Step 6: Convert Profit Percentage to Fraction
Since the options are given in fractions, we convert 2% into a fraction:
- 2% = \(\frac{2}{100} = \frac{1}{50}\)

### Final Answer
The profit percentage of the shopkeeper is \(0.02\) in decimal form or \(\frac{1}{50}\) in fractional form.

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