The average age of the present ages of Amit and Anil is 32 years. If Amit is 6 years older than Anil, what is Anil's present age?

Options

A. (a) 38 years
B. (b) 26 years
C. (c) 19 years
D. (d) 29 years

Explanation

To solve the problem, let's break it down step by step.

### Step 1: Understand the Information Given
We know:
- The average age of Amit and Anil is 32 years.
- Amit is 6 years older than Anil.

### Step 2: Set Up the Variables
Let Anil's present age be represented as \( A \).
Then, Amit's present age can be represented as \( A + 6 \) (since Amit is 6 years older than Anil).

### Step 3: Write the Equation for Average Age
The average age of Amit and Anil can be calculated using the formula:
\[ \text{Average} = \frac{\text{Sum of ages}}{\text{Number of people}} \]
In this case:
\[ 32 = \frac{A + (A + 6)}{2} \]

### Step 4: Simplify the Equation
Combine the terms in the numerator:
\[ 32 = \frac{2A + 6}{2} \]
Now, multiply both sides by 2 to eliminate the fraction:
\[ 64 = 2A + 6 \]

### Step 5: Solve for Anil's Age
Now, subtract 6 from both sides:
\[ 64 - 6 = 2A \]
\[ 58 = 2A \]
Now, divide both sides by 2:
\[ A = \frac{58}{2} = 29 \]

### Conclusion
Anil's present age is \( 29 \) years.

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