Kiran is five times as old as her niece Poonam. After five years, Kiran will be thrice as old as Poonam. Find their present ages

Answer

To find the present ages of Kiran and Poonam, we can set up a system of equations based on the information given in the problem.

### Step 1: Define the variables
Let:
- \( x \) = Kiran's present age
- \( y \) = Poonam's present age

### Step 2: Set up the equations
From the problem statement, we have two pieces of information:
1. Kiran is five times as old as Poonam:
\[ x = 5y \quad \text{(Equation 1)} \]
2. After five years, Kiran will be thrice as old as Poonam:
\[ x + 5 = 3(y + 5) \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
Now, let's simplify Equation 2:
\[ x + 5 = 3y + 15 \]
Subtracting 5 from both sides gives:
\[ x = 3y + 10 \quad \text{(Equation 3)} \]

### Step 4: Substitute Equation 1 into Equation 3
Now we can substitute Equation 1 into Equation 3:
\[ 5y = 3y + 10 \]

### Step 5: Solve for \( y \)
Now, let's solve for \( y \):
\[ 5y - 3y = 10 \]
\[ 2y = 10 \]
\[ y = 5 \]

### Step 6: Find \( x \)
Now that we have \( y \), we can find \( x \) using Equation 1:
\[ x = 5y = 5 \times 5 = 25 \]

### Conclusion
Thus, Kiran's present age is \( x = 25 \) years and Poonam's present age is \( y = 5 \) years.

### Final Answer
- Present age of Kiran: 25 years
- Present age of Poonam: 5 years

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