Step 1: Understanding the Concept:
To find the age of an additional person, calculate the total sum of ages of the group before and after that person joined.
Step 2: Key Formula or Approach:
1. \( \text{Sum of ages} = \text{Average age} \times \text{Number of people} \).
2. To find the present sum from a past average: \( \text{Present Sum} = \text{Past Sum} + (\text{Years Passed} \times \text{Number of People}) \).
Step 3: Detailed Explanation:
Five years ago:
Number of members \( = 4 \).
Average age \( = 12 \) years.
Sum of their ages 5 years ago \( = 4 \times 12 = 48 \) years.
Present sum of their ages:
Since each of the 4 members has aged by 5 years:
\[ \text{Present Sum (4 members)} = 48 + (4 \times 5) = 48 + 20 = 68 \text{ years} \] Now, a boy joins the group, so total members \( = 5 \).
New average age \( = 15 \) years.
Total sum of ages (5 people) \( = 5 \times 15 = 75 \) years.
Age of the boy \( = \text{Total sum (5 people)} - \text{Total sum (4 people)} \).
\[ \text{Age of boy} = 75 - 68 = 7 \text{ years} \]
Step 4: Final Answer:
The present age of the boy from the neighbourhood is 7 years.