Question

Average age of a nuclear family of 4 members, five years ago was 12 years. On including age of the boy from neighbourhood, the present average age is 15 years. What is the present age of the boy from the neighbourhood?

• A. 17
• B. 9
• C. 7
• D. 12

Hint:

When dealing with average age problems that span a period of time, first calculate the sum of ages at one point in time. Then, adjust this sum for the time elapsed before performing any further calculations.

Answer 1

The Correct Option is C

Step 1: Understanding the Question: 
We are given the average age of a family in the past. We need to find the age of a new person who joins the group, given the new present average age. 
Step 2: Key Formula or Approach: 
The key formula is Sum of ages = Average age \( \times \) Number of people. We will use this to find the sum of ages at different points in time. 
Step 3: Detailed Explanation: 
Part 1: Family's age five years ago. Number of family members = 4. Average age five years ago = 12 years. Sum of their ages five years ago = \(4 \times 12 = 48\) years. Part 2: Family's present age. Five years have passed, so each of the 4 members is 5 years older. Total increase in the sum of their ages = \(4 \times 5 = 20\) years. Present sum of the ages of the 4 family members = \(48 + 20 = 68\) years. 
Part 3: Including the boy. A boy from the neighbourhood joins them. New number of people = \(4 + 1 = 5\). The new present average age of the 5 people = 15 years. New sum of the present ages of all 5 people = \(5 \times 15 = 75\) years. 
Part 4: Finding the boy's age. The difference between the new total sum of ages and the family's total sum of ages will give us the boy's age. Present age of the boy = (Sum of ages of 5 people) - (Sum of ages of 4 family members) \[ \text{Boy's age} = 75 - 68 = 7 \text{ years} \] 
Step 4: Final Answer: 
The present age of the boy from the neighbourhood is 7 years.