Question

The total age of a group of 20 children is 160 years. If the average age of 8 of the children of the group is 12 years, find the average age of the remaining group.

• A. Syears
• B. 5years and 3months
• C. 5years and 4 months
• D. 5 years and 6months
• E. None of these

Answer 1

The Correct Option is C

Step 1: Understand the problem.
The total age of the group of 20 children is 160 years.
The average age of 8 of the children is 12 years.
We are asked to find the average age of the remaining 12 children.

Step 2: Calculate the total age of the 8 children.
The average age of 8 children is 12 years. The total age of these 8 children is:
Total age of 8 children = Average age × Number of children
Total age of 8 children = \( 12 \times 8 = 96 \) years.

Step 3: Calculate the total age of the remaining 12 children.
The total age of the entire group is 160 years. Therefore, the total age of the remaining 12 children is:
Total age of remaining 12 children = Total age of the group - Total age of 8 children
Total age of remaining 12 children = \( 160 - 96 = 64 \) years.

Step 4: Calculate the average age of the remaining 12 children.
The average age of the remaining 12 children is:
Average age = Total age of remaining children / Number of remaining children
Average age = \( 64 / 12 = 5.33 \) years.
\( 0.33 \) years = \( 0.33 \times 12 = 4 \) months.

Step 5: Conclusion.
The average age of the remaining 12 children is 5 years and 4 months.

Final Answer:
The correct option is (C): 5 years and 4 months.