The marked price of a watch was ₹720. A man bought the same for ₹550.80 after getting two successive discounts, the first being 10%. The second discount rate is

Options

A. 0.12
B. 0.14
C. 0.15
D. 0.18

Explanation

To find the second discount rate given the marked price and the final price after two successive discounts, we can follow these steps:

### Step 1: Calculate the first discount amount.
The marked price of the watch is ₹720, and the first discount is 10%.

First, we calculate the first discount amount:
\[ \text{First Discount} = \text{Marked Price} \times \frac{\text{Discount Rate}}{100} = 720 \times \frac{10}{100} = 72 \]

### Step 2: Calculate the price after the first discount.
Now, we subtract the first discount from the marked price to find the price after the first discount:
\[ \text{Price after First Discount} = \text{Marked Price} - \text{First Discount} = 720 - 72 = 648 \]

### Step 3: Set up the equation for the second discount.
We know the final price after both discounts is ₹550.80. Let the second discount rate be \( x\% \). The price after the second discount can be expressed as:
\[ \text{Price after Second Discount} = \text{Price after First Discount} - \text{Second Discount} \]
Where the second discount is calculated on the price after the first discount:
\[ \text{Second Discount} = \text{Price after First Discount} \times \frac{x}{100} = 648 \times \frac{x}{100} \]

Thus, we can write:
\[ 550.80 = 648 - 648 \times \frac{x}{100} \]

### Step 4: Simplify the equation.
Rearranging the equation gives:
\[ 550.80 = 648(1 - \frac{x}{100}) \]

### Step 5: Solve for \( x \).
To isolate \( x \), we first divide both sides by 648:
\[ \frac{550.80}{648} = 1 - \frac{x}{100} \]

Calculating the left side:
\[ \frac{550.80}{648} \approx 0.85 \]

Now substituting this back into the equation:
\[ 0.85 = 1 - \frac{x}{100} \]

Rearranging gives:
\[ \frac{x}{100} = 1 - 0.85 = 0.15 \]

Multiplying both sides by 100:
\[ x = 15 \]

### Final Answer:
The second discount rate is **15%**.

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