Salaries of Ankit and Ansh are in the ratio 2:3. If the salary of each is increased by Rs.4000, the new ratio becomes 40 : 57. What is Ansh's present salary?

Options

A. Rs.17,000
B. Rs.20,000
C. Rs.25,500
D. Rs.34,000

Answer

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

### Step 1: Define the Salaries
Let the salary of Ankit be \(2x\) and the salary of Ansh be \(3x\), where \(x\) is a common multiplier.

### Step 2: Set Up the New Salary Equation
According to the problem, if both salaries are increased by Rs. 4000, the new salaries will be:
- Ankit's new salary: \(2x + 4000\)
- Ansh's new salary: \(3x + 4000\)

### Step 3: Set Up the Ratio Equation
The new ratio of their salaries is given as \(40:57\). Therefore, we can set up the equation:
\[ \frac{2x + 4000}{3x + 4000} = \frac{40}{57} \]

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

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

### Step 6: Rearrange the Equation
Now, rearranging the equation to isolate \(x\):
\[ 114x - 120x = 160000 - 228000 \]
\[ -6x = -68000 \]

### Step 7: Solve for \(x\)
Dividing both sides by -6:
\[ x = \frac{68000}{6} = 11333.33 \]

### Step 8: Calculate Ansh's Salary
Now, we can find Ansh's salary:
\[ \text{Ansh's salary} = 3x = 3 \times 11333.33 = 34000 \]

### Final Answer
Thus, Ansh's present salary is **Rs. 34000**.

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