The marked price of a watch was Rs 720. A man bought the same for Rs 550.80 after getting two successive discounts, the 1st being 10%. What was the 2nd discount?

Options

A. 14%
B. 15%
C. 18%
D. 12%

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the Marked Price (MP) and Selling Price (SP)
- The marked price of the watch is given as Rs. 720.
- The selling price after discounts is Rs. 550.80.

### Step 2: Calculate the Selling Price after the First Discount
- The first discount is 10%.
- To find the selling price after the first discount (let's call it SP1), we calculate:
\[ SP1 = MP - (10\% \text{ of } MP) = MP \times (1 - \frac{10}{100}) = 720 \times 0.9 \]
- Performing the calculation:
\[ SP1 = 720 \times 0.9 = 648 \]

### Step 3: Set Up the Equation for the Second Discount
- We know that the final selling price (SP) after the second discount is Rs. 550.80.
- We can express the second discount (let's call it D2) as follows:
\[ SP = SP1 - (D2 \text{ of } SP1) \]
- Rearranging gives us:
\[ D2 = SP1 - SP \]

### Step 4: Calculate the Second Discount
- Substitute the values we have:
\[ D2 = 648 - 550.80 = 97.20 \]

### Step 5: Calculate the Percentage of the Second Discount
- To find the percentage of the second discount:
\[ \text{Percentage of } D2 = \left( \frac{D2}{SP1} \right) \times 100 = \left( \frac{97.20}{648} \right) \times 100 \]
- Performing the calculation:
\[ \text{Percentage of } D2 = \left( \frac{97.20}{648} \right) \times 100 \approx 15\% \]

### Conclusion
- The second discount is **15%**.