The ratio of the present ages of Anand and Bals is ` 8 : 3`. When Anand was 30 years old, Bala was 5 years old. Find the present age of Bala. (In years )

Options

A. 10
B. 12
C. 15
D. 20

Explanation

To find the present age of Bala, we will follow these steps:

### Step 1: Define Variables
Let the present age of Anand be \( A \) and the present age of Bala be \( B \). According to the problem, the ratio of their present ages is given as:
\[ \frac{A}{B} = \frac{8}{3} \]
This can be rewritten as:
\[ A = \frac{8}{3}B \tag{1} \]

### Step 2: Use Historical Ages
We know that when Anand was 30 years old, Bala was 5 years old. Let's denote the number of years ago when this was true as \( x \). Therefore, we can express their ages in terms of \( x \):
- Anand's age \( x \) years ago: \( A - x = 30 \)
- Bala's age \( x \) years ago: \( B - x = 5 \)

From Anand's age equation:
\[ A - x = 30 \tag{2} \]
From Bala's age equation:
\[ B - x = 5 \tag{3} \]

### Step 3: Solve for \( x \)
From equation (3), we can express \( x \) in terms of \( B \):
\[ x = B - 5 \tag{4} \]

### Step 4: Substitute \( x \) in Anand's Age Equation
Now, substitute equation (4) into equation (2):
\[ A - (B - 5) = 30 \]
This simplifies to:
\[ A - B + 5 = 30 \]
Rearranging gives us:
\[ A - B = 25 \tag{5} \]

### Step 5: Substitute \( A \) from Equation (1) into Equation (5)
Now substitute equation (1) into equation (5):
\[ \frac{8}{3}B - B = 25 \]
To combine the terms, convert \( B \) to a fraction:
\[ \frac{8}{3}B - \frac{3}{3}B = 25 \]
This simplifies to:
\[ \frac{5}{3}B = 25 \]

### Step 6: Solve for \( B \)
Multiply both sides by \( \frac{3}{5} \):
\[ B = 25 \times \frac{3}{5} = 15 \]

### Conclusion
The present age of Bala is \( \boxed{15} \) years.

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