When a discount of 20% is given on a sweater, the profit is 28%. If the discount is 14%, then the profit is

Options

A. 42 per cent
B. 46.4 per cent
C. 33.3 per cent
D. 37.6 per cent

Answer

To solve the problem step by step, we need to find the profit percentage when a discount of 14% is given on a sweater, knowing that a discount of 20% results in a profit of 28%.

### Step 1: Understand the relationship between Cost Price (CP), Selling Price (SP), and Marked Price (MP)
- Let the Cost Price (CP) of the sweater be \( CP \).
- Let the Marked Price (MP) be \( MP \).
- The Selling Price (SP) after a discount is calculated as:
\[ SP = MP - \text{Discount} \]

### Step 2: Calculate Selling Price with 20% Discount
- A 20% discount means:
\[ SP = MP \times (1 - 0.20) = MP \times 0.80 \]
- Given that this SP gives a profit of 28%, we can express this as:
\[ SP = CP \times (1 + 0.28) = CP \times 1.28 \]

### Step 3: Set up the equation
- Now we can equate the two expressions for SP:
\[ MP \times 0.80 = CP \times 1.28 \]
- Rearranging gives:
\[ MP = \frac{CP \times 1.28}{0.80} = CP \times 1.6 \]

### Step 4: Calculate Selling Price with 14% Discount
- Now, we need to find the SP when a 14% discount is applied:
\[ SP = MP \times (1 - 0.14) = MP \times 0.86 \]
- Substituting for MP from the previous step:
\[ SP = (CP \times 1.6) \times 0.86 = CP \times 1.376 \]

### Step 5: Calculate Profit Percentage
- The profit when selling at this SP is:
\[ \text{Profit} = SP - CP = CP \times 1.376 - CP = CP \times (1.376 - 1) = CP \times 0.376 \]
- The profit percentage is given by:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{CP \times 0.376}{CP} \right) \times 100 = 37.6\% \]

### Final Answer
Thus, when a discount of 14% is given on the sweater, the profit percentage is **37.6%**.

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