The salaries of Vipin and Dinesh are in the ratio 5:8. If the salary of each is increased by Rs 4,800, then new ratio becomes 7:10. What is Vipin's salary ?

Options

A. Rs 13,000
B. Rs 12,000
C. Rs 12,500
D. Rs 10,000

Answer

To find Vipin's salary, we can follow these steps:

### Step 1: Define the Salaries
Let Vipin's salary be \(5x\) and Dinesh's salary be \(8x\), based on the given ratio of their salaries.

### Step 2: Set Up the Equation for the New Salaries
When both salaries are increased by Rs 4,800, the new salaries will be:
- Vipin's new salary: \(5x + 4800\)
- Dinesh's new salary: \(8x + 4800\)

According to the problem, the new ratio of their salaries becomes \(7:10\). Therefore, we can set up the equation:
\[ \frac{5x + 4800}{8x + 4800} = \frac{7}{10} \]

### Step 3: Cross-Multiply to Eliminate the Fraction
Cross-multiplying gives us:
\[ 10(5x + 4800) = 7(8x + 4800) \]

### Step 4: Expand Both Sides
Expanding both sides results in:
\[ 50x + 48000 = 56x + 33600 \]

### Step 5: Rearrange the Equation
Now, we will rearrange the equation to isolate \(x\):
\[ 50x - 56x = 33600 - 48000 \]
\[ -6x = -14400 \]

### Step 6: Solve for \(x\)
Dividing both sides by -6 gives:
\[ x = \frac{14400}{6} = 2400 \]

### Step 7: Calculate Vipin's Salary
Now that we have \(x\), we can find Vipin's salary:
\[ \text{Vipin's salary} = 5x = 5 \times 2400 = 12000 \]

### Conclusion
Vipin's salary is Rs 12,000.

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