The marked price of a watch is Rs 1600. After two successive discounts it is sold for Rs 1224. If the rate of first discount is 10%. What is the rate of second discount?

Answer

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

### Step 1: Identify the given values
- Marked Price (MP) = Rs 1600
- Selling Price (SP) after two discounts = Rs 1224
- First Discount Rate = 10%

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

First, we need to find the amount of the first discount:
\[ \text{First Discount} = \text{MP} \times \frac{\text{First Discount Rate}}{100} = 1600 \times \frac{10}{100} = 160 \text{ Rs} \]

Now, subtract the first discount from the marked price to find the selling price after the first discount:
\[ \text{SP after first discount} = \text{MP} - \text{First Discount} = 1600 - 160 = 1440 \text{ Rs} \]

### Step 3: Calculate the second discount
We know the final selling price after two discounts is Rs 1224. We can find the second discount by subtracting the selling price after the first discount from the final selling price:
\[ \text{Second Discount Amount} = \text{SP after first discount} - \text{Final SP} = 1440 - 1224 = 216 \text{ Rs} \]

### Step 4: Calculate the rate of the second discount
To find the rate of the second discount, we use the amount of the second discount and the selling price after the first discount:
\[ \text{Rate of Second Discount} = \left(\frac{\text{Second Discount Amount}}{\text{SP after first discount}}\right) \times 100 \]
Substituting the values:
\[ \text{Rate of Second Discount} = \left(\frac{216}{1440}\right) \times 100 \]

Now calculate:
\[ \text{Rate of Second Discount} = \left(\frac{216 \times 100}{1440}\right) = \frac{21600}{1440} = 15\% \]

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

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