The monthly salaries of A and B are in the ratio 6:7. If both of them get a salary increment of Rs 5000 per month, the new ratio becomes 7:8. What is the new monthly salary of A ?

Options

A. Rs 30000
B. Rs 32000
C. Rs 35000
D. Rs 40000

Answer

To solve the problem, let's break it down step by step.

### Step 1: Define the Salaries
Let the monthly salaries of A and B be represented as:
- Salary of A = 6x
- Salary of B = 7x

### Step 2: Set Up the New Salaries After Increment
After both A and B receive a salary increment of Rs 5000, their new salaries will be:
- New Salary of A = 6x + 5000
- New Salary of B = 7x + 5000

### Step 3: Set Up the New Ratio
According to the problem, the new ratio of their salaries becomes 7:8. Therefore, we can set up the equation:
\[ \frac{6x + 5000}{7x + 5000} = \frac{7}{8} \]

### Step 4: Cross Multiply to Solve for x
Cross-multiplying gives us:
\[ 8(6x + 5000) = 7(7x + 5000) \]
Expanding both sides:
\[ 48x + 40000 = 49x + 35000 \]

### Step 5: Rearrange the Equation
Now, rearranging the equation to isolate x:
\[ 48x + 40000 - 35000 = 49x \]
\[ 40000 - 35000 = 49x - 48x \]
\[ 5000 = x \]

### Step 6: Calculate the New Salary of A
Now that we have the value of x, we can find the new salary of A:
- Original Salary of A = 6x = 6 * 5000 = Rs 30000
- New Salary of A = 6x + 5000 = 30000 + 5000 = Rs 35000

### Final Answer
The new monthly salary of A is **Rs 35000**.

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