The marked price of a washing machine is Rs.7,200.if it sold for ₹5,512.50 after two successive discounts of x % each . The value of x is

Options

A. 12
B. 12.5
C. 10.5
D. 15

Answer

To find the value of \( x \) in the given problem, we will follow these steps:

### Step 1: Understand the Problem
We know:
- Marked Price (MP) = Rs. 7200
- Selling Price (SP) = Rs. 5512.50
- There are two successive discounts of \( x\% \).

### Step 2: Set Up the Equation
When a discount of \( x\% \) is applied to the marked price, the price after the first discount can be expressed as:
\[ \text{Price after first discount} = MP \times \left(1 - \frac{x}{100}\right) = 7200 \times \left(1 - \frac{x}{100}\right) \]

After applying the second discount of \( x\% \) on the new price:
\[ \text{Selling Price} = \text{Price after first discount} \times \left(1 - \frac{x}{100}\right) = 7200 \times \left(1 - \frac{x}{100}\right) \times \left(1 - \frac{x}{100}\right) \]
This simplifies to:
\[ SP = 7200 \times \left(1 - \frac{x}{100}\right)^2 \]

### Step 3: Substitute the Selling Price
Substituting the known selling price into the equation:
\[ 5512.50 = 7200 \times \left(1 - \frac{x}{100}\right)^2 \]

### Step 4: Solve for \( \left(1 - \frac{x}{100}\right)^2 \)
Dividing both sides by 7200:
\[ \left(1 - \frac{x}{100}\right)^2 = \frac{5512.50}{7200} \]
Calculating the right-hand side:
\[ \left(1 - \frac{x}{100}\right)^2 = 0.765625 \]

### Step 5: Take the Square Root
Taking the square root of both sides:
\[ 1 - \frac{x}{100} = \sqrt{0.765625} \]
Calculating the square root:
\[ 1 - \frac{x}{100} = 0.875 \]

### Step 6: Solve for \( x \)
Rearranging the equation:
\[ \frac{x}{100} = 1 - 0.875 \]
\[ \frac{x}{100} = 0.125 \]
Multiplying both sides by 100:
\[ x = 12.5 \]

### Conclusion
The value of \( x \) is \( 12.5\% \).