The monthly salaries of two persons are in the ratio of `4 : 7`. If each receives an increase of Rs. 25 in the salary the ratio is altered to `3 : 5`. Find their respective salaries.

Options

A. 120 & 210
B. 80 & 140
C. 180 & 300
D. 200 & 350

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Salaries
Let the monthly salaries of the two persons be represented as:
- Salary of the first person = 4x
- Salary of the second person = 7x

### Step 2: Account for the Increase in Salary
Both persons receive an increase of Rs. 25 in their salaries. Therefore, after the increase, their salaries will be:
- New salary of the first person = 4x + 25
- New salary of the second person = 7x + 25

### Step 3: Set Up the New Ratio
According to the problem, after the increase, the ratio of their salaries changes to 3:5. We can set up the equation:
\[ \frac{4x + 25}{7x + 25} = \frac{3}{5} \]

### Step 4: Cross-Multiply to Solve for x
Cross-multiplying gives us:
\[ 5(4x + 25) = 3(7x + 25) \]
Expanding both sides:
\[ 20x + 125 = 21x + 75 \]

### Step 5: Rearrange the Equation
Now, rearranging the equation to isolate x:
\[ 20x + 125 - 75 = 21x \]
\[ 50 = 21x - 20x \]
\[ 50 = x \]

### Step 6: Calculate the Salaries
Now that we have the value of x, we can find the respective salaries:
- Salary of the first person = 4x = 4 * 50 = Rs. 200
- Salary of the second person = 7x = 7 * 50 = Rs. 350

### Step 7: Conclusion
Thus, the respective salaries of the two persons are:
- First person: Rs. 200
- Second person: Rs. 350

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