Two years ago, Mohit was three times as old as his son and two years hence, twice of Mohit's age will be equal to five times that of his son. The present age of Mohit is ____

Options

A. 14 years
B. 38 years
C. 32 years
D. 34 years

Answer

To solve the problem step by step, we will set up equations based on the information given in the question.

### Step 1: Define Variables
Let:
- \( x \) = Present age of Mohit
- \( y \) = Present age of Mohit's son

### Step 2: Set Up the First Equation
According to the problem, two years ago, Mohit was three times as old as his son. Therefore, we can write:
\[ x - 2 = 3(y - 2) \]
Expanding this gives:
\[ x - 2 = 3y - 6 \]
Rearranging it, we get:
\[ x - 3y = -4 \quad \text{(Equation 1)} \]

### Step 3: Set Up the Second Equation
The problem also states that two years hence, twice Mohit's age will be equal to five times his son's age. Therefore, we can write:
\[ 2(x + 2) = 5(y + 2) \]
Expanding this gives:
\[ 2x + 4 = 5y + 10 \]
Rearranging it, we get:
\[ 2x - 5y = 6 \quad \text{(Equation 2)} \]

### Step 4: Solve the System of Equations
Now we have a system of two equations:
1. \( x - 3y = -4 \) (Equation 1)
2. \( 2x - 5y = 6 \) (Equation 2)

We can multiply Equation 1 by 2 to eliminate \( x \):
\[ 2(x - 3y) = 2(-4) \]
This simplifies to:
\[ 2x - 6y = -8 \quad \text{(Equation 3)} \]

### Step 5: Subtract Equation 2 from Equation 3
Now we will subtract Equation 2 from Equation 3:
\[ (2x - 6y) - (2x - 5y) = -8 - 6 \]
This simplifies to:
\[ -y = -14 \]
Thus, we find:
\[ y = 14 \]

### Step 6: Substitute \( y \) Back to Find \( x \)
Now we substitute \( y = 14 \) back into Equation 1 to find \( x \):
\[ x - 3(14) = -4 \]
This simplifies to:
\[ x - 42 = -4 \]
Adding 42 to both sides gives:
\[ x = 38 \]

### Conclusion
The present age of Mohit is \( \boxed{38} \).