Sumit is 3 times as old as his son. Five years later, he shall be two and half times as old as his son. How old is Sumit at present?

Answer

To solve the problem, we will set up a system of equations based on the information given.

### Step 1: Define Variables
Let:
- \( S \) = present age of Sumit
- \( s \) = present age of Sumit's son

### Step 2: Set Up the First Equation
According to the problem, Sumit is 3 times as old as his son. This can be expressed as:
\[ S = 3s \]
(Equation 1)

### Step 3: Set Up the Second Equation
Five years later, Sumit will be two and a half times as old as his son. In five years, their ages will be:
- Sumit's age: \( S + 5 \)
- Son's age: \( s + 5 \)

The relationship can be expressed as:
\[ S + 5 = 2.5(s + 5) \]
(Equation 2)

### Step 4: Simplify Equation 2
Now, let's simplify Equation 2:
\[ S + 5 = 2.5s + 12.5 \]
Subtracting 5 from both sides gives:
\[ S = 2.5s + 7.5 \]
(Equation 3)

### Step 5: Substitute Equation 1 into Equation 3
Now we will substitute Equation 1 into Equation 3:
From Equation 1, we know \( S = 3s \). Replacing \( S \) in Equation 3:
\[ 3s = 2.5s + 7.5 \]

### Step 6: Solve for \( s \)
Now, let's isolate \( s \):
\[ 3s - 2.5s = 7.5 \]
\[ 0.5s = 7.5 \]
Dividing both sides by 0.5 gives:
\[ s = 15 \]

### Step 7: Find Sumit's Age
Now that we have the son's age, we can find Sumit's age using Equation 1:
\[ S = 3s = 3 \times 15 = 45 \]

### Conclusion
Thus, Sumit's present age is:
\[ \boxed{45} \]

---