A dealer marks his goods `20%` above cost price. He then allows some discount on it and makes a profit of `8%`. The rate of discount is-

Options

A. `12%`
B. `10%`
C. `6%`
D. `4%`

Answer

To solve the problem step by step, we will use the relationship between Cost Price (CP), Marked Price (MP), Selling Price (SP), profit, and discount.

### Step 1: Understand the relationship between CP, MP, SP, profit, and discount.
- The dealer marks his goods 20% above the cost price. This means:
\[ MP = CP + 20\% \text{ of } CP = CP + 0.2 \times CP = 1.2 \times CP \]

### Step 2: Calculate the Selling Price (SP) based on the profit.
- The dealer makes a profit of 8% on the cost price. Therefore:
\[ SP = CP + 8\% \text{ of } CP = CP + 0.08 \times CP = 1.08 \times CP \]

### Step 3: Set up the equation using the relationship between MP, SP, and discount.
- The relationship can be expressed as:
\[ SP = MP \times \left(1 - \frac{D}{100}\right) \]
where \(D\) is the discount percentage.

### Step 4: Substitute the values of MP and SP into the equation.
- From Step 1, we know \(MP = 1.2 \times CP\) and from Step 2, we know \(SP = 1.08 \times CP\). Substituting these into the equation gives:
\[ 1.08 \times CP = (1.2 \times CP) \times \left(1 - \frac{D}{100}\right) \]

### Step 5: Cancel \(CP\) from both sides of the equation.
- Since \(CP\) is common on both sides and not equal to zero, we can cancel it:
\[ 1.08 = 1.2 \times \left(1 - \frac{D}{100}\right) \]

### Step 6: Solve for \(D\).
- Rearranging the equation gives:
\[ 1 - \frac{D}{100} = \frac{1.08}{1.2} \]
- Calculate \(\frac{1.08}{1.2}\):
\[ \frac{1.08}{1.2} = 0.9 \]
- Therefore:
\[ 1 - \frac{D}{100} = 0.9 \]
- Rearranging gives:
\[ \frac{D}{100} = 1 - 0.9 = 0.1 \]
- Thus:
\[ D = 0.1 \times 100 = 10\% \]

### Conclusion:
The rate of discount is **10%**.

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