Salaries of Rajesh and Sunil are in the ratio of 2 :3. If the salary of each one is increased by Rs. 4000 the new ratio becomes 40 : 57. What is Sunil’s present salary ?

Options

A. Rs 17000
B. Rs 20000
C. Rs 25500
D. None of these

Answer

To solve the problem step by step, we will follow the information provided in the question and derive the necessary equations to find Sunil's present salary.

### Step 1: Define the Salaries
Let the present salary of Rajesh be \( 2k \) and the present salary of Sunil be \( 3k \), where \( k \) is a common factor.

### Step 2: Set Up the New Salaries After Increase
According to the problem, both Rajesh and Sunil's salaries are increased by Rs. 4000. Therefore, the new salaries will be:
- Rajesh's new salary = \( 2k + 4000 \)
- Sunil's new salary = \( 3k + 4000 \)

### Step 3: Write the New Ratio
After the increase, the new ratio of their salaries is given as 40:57. We can set up the equation:
\[ \frac{2k + 4000}{3k + 4000} = \frac{40}{57} \]

### Step 4: Cross-Multiply to Eliminate the Fraction
Cross-multiplying gives us:
\[ 57(2k + 4000) = 40(3k + 4000) \]

### Step 5: Expand Both Sides
Expanding both sides results in:
\[ 114k + 228000 = 120k + 160000 \]

### Step 6: Rearrange the Equation
Now, we will rearrange the equation to isolate \( k \):
\[ 114k + 228000 - 160000 = 120k \]
\[ 114k + 68000 = 120k \]

### Step 7: Solve for \( k \)
Subtract \( 114k \) from both sides:
\[ 68000 = 120k - 114k \]
\[ 68000 = 6k \]
Now, divide both sides by 6:
\[ k = \frac{68000}{6} = 11333.33 \]

### Step 8: Calculate Sunil's Present Salary
Now that we have \( k \), we can find Sunil's present salary:
\[ \text{Sunil's salary} = 3k = 3 \times 11333.33 = 34000 \]

### Conclusion
Thus, Sunil's present salary is Rs. 34,000.