The average age of 60 boys in a class was calculated as 12 years. It was later realised that the actual age of one of the boys in the class was 12.5 years but it was calculated as 14 years. What is the actual average age of the boys in the class ?

Options

A. 11 years
B. 11.275 years
C. 11.50 years
D. 11.975 years

Explanation

To find the actual average age of the boys in the class, we need to follow these steps:

### Step 1: Calculate the initial sum of ages based on the average
The average age of the 60 boys is given as 12 years. We can calculate the total sum of their ages (S) using the formula for average:

\[ \text{Average} = \frac{\text{Sum of ages}}{\text{Number of boys}} \]

Thus, we have:

\[ 12 = \frac{S}{60} \]

To find S, we multiply both sides by 60:

\[ S = 12 \times 60 = 720 \]

### Step 2: Identify the error in the age calculation
It was later realized that one boy's age was recorded incorrectly. His actual age is 12.5 years, but it was mistakenly recorded as 14 years.

### Step 3: Calculate the difference due to the error
The difference between the recorded age and the actual age is:

\[ \text{Difference} = 14 - 12.5 = 1.5 \]

### Step 4: Adjust the sum of ages to account for the error
Since the recorded age was higher than the actual age, we need to subtract this difference from the total sum of ages:

\[ \text{New Sum} = S - \text{Difference} = 720 - 1.5 = 718.5 \]

### Step 5: Calculate the new average age
Now, we can find the new average age using the adjusted sum:

\[ \text{New Average} = \frac{\text{New Sum}}{\text{Number of boys}} = \frac{718.5}{60} \]

Calculating this gives:

\[ \text{New Average} = 11.975 \]

### Conclusion
The actual average age of the boys in the class is **11.975 years**.

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