The list price of a clock is Rs. 160. A customer buys is for 122.40 after two successve discounts. If first discount is 10%, the second is

Options

A. `10%`
B. `12%`
C. `15%`
D. `18%`

Answer

To solve the problem step by step, we will determine the second discount percentage given the first discount and the final selling price.

### Step-by-Step Solution:

1. **Identify the List Price (Marked Price)**:
- The list price of the clock is given as Rs. 160.

2. **Calculate the First Discount**:
- The first discount is 10% of the list price.
- First discount = 10% of 160 = (10/100) * 160 = Rs. 16.

3. **Calculate the Selling Price After First Discount**:
- Selling Price after first discount = List Price - First Discount.
- Selling Price after first discount = 160 - 16 = Rs. 144.

4. **Identify the Final Selling Price**:
- The customer buys the clock for Rs. 122.40.

5. **Calculate the Difference Between Selling Price After First Discount and Final Selling Price**:
- Difference = Selling Price after first discount - Final Selling Price.
- Difference = 144 - 122.40 = Rs. 21.60.

6. **Calculate the Second Discount Percentage**:
- The second discount is based on the selling price after the first discount.
- Second Discount Percentage = (Second Discount / Selling Price after first discount) * 100.
- Here, Second Discount = Rs. 21.60 and Selling Price after first discount = Rs. 144.
- Second Discount Percentage = (21.60 / 144) * 100.

7. **Perform the Calculation**:
- Second Discount Percentage = (21.60 / 144) * 100 = (21.60 * 100) / 144.
- Simplifying this:
- 21.60 * 100 = 2160.
- Now divide 2160 by 144.
- 2160 ÷ 144 = 15.

8. **Final Result**:
- The second discount percentage is 15%.

### Summary:
- The second discount percentage is **15%**.