On the April 2018, my salary increased from `1,00,000` to x and the rate of income tax decreased by `37.5%` so the amount of income tax paid by me remains constant and the diff.in the rate of income tax is `9%`. Find the value of x ?

Options

A. `1,65,000`
B. `1,55,000`
C. `1,60,000`
D. `1,22,000`

Answer

To solve the problem step by step, we need to analyze the information given and apply the concepts of percentage and income tax.

### Step 1: Understand the initial conditions
- Initial salary = ₹1,00,000
- Initial income tax rate = 9%
- Therefore, initial income tax paid = 9% of ₹1,00,000

**Calculation:**
\[ \text{Initial Income Tax} = \frac{9}{100} \times 1,00,000 = ₹9,000 \]

**Hint:** Calculate the initial income tax by applying the percentage to the initial salary.

### Step 2: Determine the new rate of income tax
- The rate of income tax decreased by 37.5%.
- New rate of income tax = Initial rate - Decrease in rate

**Calculation:**
\[ \text{Decrease in rate} = 37.5\% \text{ of } 9\% = \frac{37.5}{100} \times 9 = 3.375\% \]
\[ \text{New rate} = 9\% - 3.375\% = 5.625\% \]

**Hint:** Calculate the decrease in the income tax rate by applying the percentage to the initial rate.

### Step 3: Relate the new salary to the constant income tax paid
- The amount of income tax paid remains constant at ₹9,000.
- Let the new salary be x. The new income tax paid can be expressed as:
\[ \text{New Income Tax} = \text{New Rate} \times \text{New Salary} = 5.625\% \text{ of } x \]
\[ \frac{5.625}{100} \times x = 9,000 \]

**Hint:** Set up the equation for the new income tax using the new rate and the new salary.

### Step 4: Solve for x
- Rearranging the equation gives:
\[ x = \frac{9,000 \times 100}{5.625} \]

**Calculation:**
\[ x = \frac{9,00,000}{5.625} = 1,60,000 \]

**Hint:** Perform the division carefully to find the new salary.

### Conclusion
The value of x (the new salary) is ₹1,60,000.

**Final Answer:** ₹1,60,000