Raje's salary was first increased by `10%` then decreased by `20%` If the latest salary is `Rs 17600, then find his orginal salary.

Options

A. Rs. 15000
B. Rs. 10000
C. Rs. 20000
D. Rs. 18000

Explanation

To find Raje's original salary, we will follow these steps:

### Step 1: Let the original salary be represented as \( x \).
We will denote Raje's original salary as \( x \).

### Step 2: Calculate the salary after a 10% increase.
When Raje's salary is increased by 10%, the new salary can be calculated as:
\[ \text{New Salary} = x + \frac{10}{100} \times x = x + 0.1x = 1.1x \]

### Step 3: Calculate the salary after a 20% decrease.
Next, Raje's salary is decreased by 20%. The amount of decrease can be calculated from the new salary:
\[ \text{Decrease} = \frac{20}{100} \times 1.1x = 0.2 \times 1.1x = 0.22x \]
Thus, the salary after the decrease will be:
\[ \text{Latest Salary} = 1.1x - 0.22x = 0.88x \]

### Step 4: Set up the equation with the latest salary.
According to the problem, Raje's latest salary is \( Rs. 17600 \). Therefore, we can set up the equation:
\[ 0.88x = 17600 \]

### Step 5: Solve for \( x \).
To find \( x \), we divide both sides of the equation by 0.88:
\[ x = \frac{17600}{0.88} \]
Calculating this gives:
\[ x = 20000 \]

### Conclusion:
Raje's original salary is \( Rs. 20000 \).

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