The marked price of a watch was Rs. 720/- A man bought the same for Rs. 550.80, after getting two successive discounts, the first at 10%. What was the second discount rate ?

Options

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

Answer

To find the second discount rate, we will follow these steps:

### Step 1: Calculate the first discount amount
The marked price (MP) of the watch is Rs. 720. The first discount (D1) is 10%.

First, we calculate the amount of the first discount:
\[ D1 = \text{MP} \times \frac{10}{100} = 720 \times 0.10 = 72 \]

### Step 2: Calculate the selling price after the first discount
Now, we subtract the first discount from the marked price to find the selling price after the first discount (SP1):
\[ SP1 = \text{MP} - D1 = 720 - 72 = 648 \]

### Step 3: Calculate the difference between the selling price and the actual price
The man bought the watch for Rs. 550.80. We need to find the difference between SP1 and the actual selling price (SP):
\[ \text{Difference} = SP1 - \text{Actual Price} = 648 - 550.80 = 97.20 \]

### Step 4: Calculate the second discount percentage
Now, we need to find the second discount (D2) as a percentage of SP1. The formula for the second discount percentage is:
\[ D2\% = \left( \frac{\text{Difference}}{SP1} \right) \times 100 \]
Substituting the values we have:
\[ D2\% = \left( \frac{97.20}{648} \right) \times 100 \]

### Step 5: Solve for D2%
Calculating the above expression:
\[ D2\% = \left( \frac{97.20}{648} \right) \times 100 \approx 15 \]

Thus, the second discount rate is approximately **15%**.

### Summary of Steps:
1. Calculate the first discount amount (10% of Rs. 720).
2. Subtract the first discount from the marked price to find the selling price after the first discount.
3. Find the difference between the selling price after the first discount and the actual selling price.
4. Use the difference to calculate the second discount percentage based on the selling price after the first discount.