The average age of a family of 5 members, three years ago, was 17 years. Inspite of the birth of a child in the family during these 3 years the present average age of the family remains the same. What is the present age of the child ?
2 years
To solve the problem, we need to determine the present age of the child born during the past three years.
- Three years ago, the average age of a family consisting of 5 members was 17 years.
- The total age of the family members three years ago can be calculated as:
\(17 \times 5 = 85 \text{ years}\) - After three years, each of the original 5 members has aged by 3 years, so the total age increase for them is:
\(5 \times 3 = 15 \text{ years}\) - Thus, the current total age of the original 5 family members is:
\(85 + 15 = 100 \text{ years}\) - In the present, the average age of the family is still given as 17 years. This is now the average for 6 members (the original 5 plus the new child).
- The current total age of the family (6 members) is:
\(17 \times 6 = 102 \text{ years}\) - The present age of the child will be the difference between the total current age of the family and the total current age of the original 5 members:
\(102 - 100 = 2 \text{ years}\) - Thus, the present age of the child is 2 years.
Therefore, the correct answer is 2 years.
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