The marked price of a watch is Rs. 800. A shopkeeper gives two successive discounts and sells the watch at Rs. 612. If the first discount is 10%, the second discount is

Options

A. a. 12%
B. b. 20%
C. c. 15%
D. d. 10%

Answer

To find the second discount given the marked price, first discount, and selling price, we can follow these steps:

### Step 1: Identify the given values
- Marked Price (MP) = Rs. 800
- Selling Price (SP) = Rs. 612
- First Discount (D1) = 10%

### Step 2: Calculate the first discount amount
The first discount is 10% of the marked price.

\[ \text{First Discount} (D1) = \frac{10}{100} \times \text{MP} = \frac{10}{100} \times 800 = 80 \text{ Rs.} \]

### Step 3: Calculate the price after the first discount
To find the price after the first discount, subtract the first discount from the marked price.

\[ \text{Price after first discount} = \text{MP} - D1 = 800 - 80 = 720 \text{ Rs.} \]

### Step 4: Calculate the total discount given
The total discount can be calculated by subtracting the selling price from the price after the first discount.

\[ \text{Total Discount} = \text{Price after first discount} - \text{SP} = 720 - 612 = 108 \text{ Rs.} \]

### Step 5: Calculate the second discount percentage
The second discount can be calculated as a percentage of the price after the first discount.

\[ \text{Second Discount} (D2) = \frac{\text{Total Discount}}{\text{Price after first discount}} \times 100 = \frac{108}{720} \times 100 \]

Calculating this gives:

\[ D2 = \frac{108 \times 100}{720} = 15\% \]

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

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