The marked price of a clock is 3200. It is to be sold at 2448 at two successive discounts. If the first discount is 10%, then the second discount is

Options

A. 0.05
B. 0.1
C. 0.15
D. 0.2

Answer

To solve the problem step by step, we need to find the second discount after applying the first discount of 10% on the marked price of the clock.

### Step-by-Step Solution:

1. **Identify the Marked Price (MP)**:
The marked price of the clock is given as:
\[ MP = 3200 \]

2. **Calculate the First Discount**:
The first discount is 10% of the marked price. We can calculate the amount of the first discount:
\[ \text{First Discount} = \frac{10}{100} \times 3200 = 320 \]

3. **Calculate the Selling Price after the First Discount**:
To find the selling price after the first discount, we subtract the first discount from the marked price:
\[ SP_1 = MP - \text{First Discount} = 3200 - 320 = 2880 \]

4. **Identify the Final Selling Price (SP)**:
The final selling price after the second discount is given as:
\[ SP = 2448 \]

5. **Calculate the Difference between SP1 and SP**:
Now, we find the difference between the selling price after the first discount and the final selling price:
\[ \text{Difference} = SP_1 - SP = 2880 - 2448 = 432 \]

6. **Calculate the Second Selling Price**:
The selling price after the first discount is $2880, and the final selling price is $2448. The difference of $432 represents the amount of the second discount.

7. **Calculate the Second Discount Percentage**:
To find the percentage of the second discount, we use the selling price after the first discount:
\[ \text{Second Discount Percentage} = \left(\frac{\text{Difference}}{SP_1}\right) \times 100 = \left(\frac{432}{2880}\right) \times 100 \]
\[ = 15\% \]

8. **Convert the Percentage to Decimal**:
To express the second discount as a decimal:
\[ 15\% = \frac{15}{100} = 0.15 \]

### Final Answer:
The second discount is **0.15**.

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