The monthly salaries of A and B are in the ratio 9:10. If both of them get a salary increment of Rs 6000 per month, the new ratio becomes 21:23. What is the new monthly salary of A?

Options

A. a)Rs 38000
B. b)Rs 40000
C. c)Rs 46000
D. d)Rs 42000

Answer

To solve the problem step by step, we will denote the salaries of A and B using variables based on the given ratio.

### Step 1: Define the Salaries
Let the monthly salary of A be \( 9x \) and the monthly salary of B be \( 10x \), where \( x \) is a common multiplier.

### Step 2: Apply the Salary Increment
Both A and B receive an increment of Rs 6000. Therefore, the new salaries will be:
- New salary of A: \( 9x + 6000 \)
- New salary of B: \( 10x + 6000 \)

### Step 3: Set Up the New Ratio
According to the problem, the new ratio of their salaries becomes \( 21:23 \). We can express this as:
\[ \frac{9x + 6000}{10x + 6000} = \frac{21}{23} \]

### Step 4: Cross-Multiply to Eliminate the Fraction
Cross-multiplying gives us:
\[ 23(9x + 6000) = 21(10x + 6000) \]

### Step 5: Expand Both Sides
Expanding both sides results in:
\[ 207x + 138000 = 210x + 126000 \]

### Step 6: Rearrange the Equation
Rearranging the equation to isolate \( x \):
\[ 207x - 210x = 126000 - 138000 \]
\[ -3x = -12000 \]

### Step 7: Solve for \( x \)
Dividing both sides by -3 gives:
\[ x = 4000 \]

### Step 8: Calculate the New Salary of A
Now we can find the new salary of A:
- Original salary of A: \( 9x = 9 \times 4000 = 36000 \)
- New salary of A after the increment: \( 36000 + 6000 = 42000 \)

### Final Answer
The new monthly salary of A is **Rs 42,000**.

---