The ratio of the salaries of A and B is `8:9` If A's salary is increaed by `50%` and B's salary is reduced by `25%`, their ratio becomes `16:9`. What is the salary of A ?

Options

A. `₹22000`
B. `₹ 28500`
C. `₹ 37000`
D. Cannot be determined

Explanation

To solve the problem step by step, we will use the given ratios and perform calculations based on the changes in salaries.

### Step-by-Step Solution:

1. **Define the Salaries**:
Let the salaries of A and B be represented as:
\[ A = 8x \quad \text{and} \quad B = 9x \]
where \(x\) is a common multiplier.

**Hint**: Start by expressing the salaries in terms of a variable based on the given ratio.

2. **Calculate A's New Salary**:
A's salary is increased by 50%. Therefore, the increase can be calculated as:
\[ \text{Increase} = 50\% \text{ of } A = 0.5 \times 8x = 4x \]
Thus, A's new salary becomes:
\[ A' = A + \text{Increase} = 8x + 4x = 12x \]

**Hint**: Remember to calculate the increase based on the percentage given.

3. **Calculate B's New Salary**:
B's salary is reduced by 25%. The reduction can be calculated as:
\[ \text{Reduction} = 25\% \text{ of } B = 0.25 \times 9x = \frac{9x}{4} \]
Therefore, B's new salary becomes:
\[ B' = B - \text{Reduction} = 9x - \frac{9x}{4} = \frac{36x}{4} - \frac{9x}{4} = \frac{27x}{4} \]

**Hint**: When calculating the reduction, ensure you subtract it from the original salary.

4. **Set Up the New Ratio**:
According to the problem, the new ratio of A's salary to B's salary is given as:
\[ \frac{A'}{B'} = \frac{16}{9} \]
Substituting the new salaries:
\[ \frac{12x}{\frac{27x}{4}} = \frac{16}{9} \]

**Hint**: Set up the equation using the new salaries and the given ratio.

5. **Cross-Multiply to Solve for x**:
Cross-multiplying gives:
\[ 12x \cdot 9 = 16 \cdot \frac{27x}{4} \]
Simplifying this:
\[ 108x = 108x \]
This simplifies to:
\[ 108x = 108x \]
This means the equation holds true for any value of \(x\).

**Hint**: Cross-multiplication is a useful technique for solving ratios.

6. **Find A's Salary**:
Since we need to find A's salary, we can express it as:
\[ A = 8x \]
To find the actual salary, we need to choose a value for \(x\). Since the ratio holds for any \(x\), we can set \(x = 1\) for simplicity:
\[ A = 8 \times 1 = 8 \]

**Hint**: Choose a simple value for \(x\) to calculate the actual salary.

### Final Answer:
The salary of A is \(8\) (in whatever currency unit is applicable).