A dealer marks his goods 25% above the cost price. He, then allows some discount on it and makes a profit of 10%. Find the rate of discount.

Options

A. 12%
B. 13%
C. 15%
D. 16%

Answer

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step 1: Assume the Cost Price
Let’s assume the cost price (CP) of the goods is \(100\).

### Step 2: Calculate the Marked Price
The dealer marks his goods 25% above the cost price.
\[ \text{Marked Price (MP)} = \text{Cost Price} + 25\% \text{ of Cost Price} = 100 + 25\% \times 100 = 100 + 25 = 125 \]

### Step 3: Determine the Selling Price
The dealer makes a profit of 10% on the cost price.
\[ \text{Selling Price (SP)} = \text{Cost Price} + 10\% \text{ of Cost Price} = 100 + 10\% \times 100 = 100 + 10 = 110 \]

### Step 4: Calculate the Discount
The discount (D) can be calculated using the formula:
\[ \text{Discount} = \text{Marked Price} - \text{Selling Price} = 125 - 110 = 15 \]

### Step 5: Calculate the Discount Percentage
The discount percentage is calculated based on the marked price:
\[ \text{Discount Percentage} = \left( \frac{\text{Discount}}{\text{Marked Price}} \right) \times 100 = \left( \frac{15}{125} \right) \times 100 \]
Calculating this gives:
\[ \text{Discount Percentage} = \left( \frac{15 \times 100}{125} \right) = \left( \frac{1500}{125} \right) = 12\% \]

### Conclusion
Thus, the rate of discount is \(12\%\).

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