The marked price of a watch is Rs. 1,600. The shopkeeper gives succesive discounts of 10% and x% to the customer. If the customer pays Rs. 1,224 for the watch, the value of x is

Options

A. `5%`
B. `10%`
C. `15%`
D. `20%`

Answer

To solve the problem step by step, we need to find the value of x% discount that, when applied successively with a 10% discount on the marked price of a watch, results in a final price of Rs. 1,224.

### Step 1: Calculate the price after the first discount of 10%
The marked price (MP) of the watch is Rs. 1,600. The first discount is 10%.

To find the price after the first discount:
\[ \text{Price after 10% discount} = \text{MP} - (\text{MP} \times \text{Discount Percentage}) \]
\[ = 1600 - (1600 \times 0.10) \]
\[ = 1600 - 160 \]
\[ = 1440 \]

### Step 2: Set up the equation for the second discount of x%
After the first discount, the price of the watch is Rs. 1,440. Now, we apply the second discount of x%.

The price after the second discount can be expressed as:
\[ \text{Final Price} = \text{Price after first discount} - (\text{Price after first discount} \times \frac{x}{100}) \]
This can be rewritten as:
\[ 1224 = 1440 - (1440 \times \frac{x}{100}) \]

### Step 3: Rearranging the equation
Now, we can rearrange the equation to isolate x:
\[ 1224 = 1440 \left(1 - \frac{x}{100}\right) \]
Dividing both sides by 1440:
\[ \frac{1224}{1440} = 1 - \frac{x}{100} \]
Calculating the left side:
\[ \frac{1224}{1440} = 0.85 \]
So, we have:
\[ 0.85 = 1 - \frac{x}{100} \]

### Step 4: Solve for x
Rearranging gives:
\[ \frac{x}{100} = 1 - 0.85 \]
\[ \frac{x}{100} = 0.15 \]
Multiplying both sides by 100:
\[ x = 15 \]

### Conclusion
The value of x is 15%.