The sum of the ages of 5 members comprising a family, 3 years ago was 80 years. The average age of the family today is the same as it was 3 years ago, because of an addition of a baby during the intervening period. How old is the baby ?

(a) 6 months
(b) 1 year ✓ UPSC's answer
(c) 2 years
(d) 2 years and 6 months

Why the answer is (b)

• Three years ago, the sum of the ages of the 5 family members was 80 years, making the average age 80/5 = 16 years.

• Today, those same 5 members have each aged by 3 years, so their current combined age is 80 + (5 * 3) = 95 years.

• The problem states the average age of the family today is the same as it was 3 years ago, which is 16 years.

• Since a baby was added, the family now has 6 members. The total sum of ages for 6 members with an average of 16 is 6 * 16 = 96 years.

• The baby's age is the difference between the new total sum (96) and the sum of the original 5 members' current ages (95), which is 96 - 95 = 1 year.

• Therefore, the baby is 1 year old, corresponding to option (b).

Why the other options are wrong

(a) 6 months: A 6-month-old baby would result in a total family age of 95.5 years, giving an average of approximately 15.92 years, not 16.
(c) 2 years: A 2-year-old baby would result in a total family age of 97 years, giving an average of approximately 16.17 years, not 16.
(d) 2 years and 6 months: A 2.5-year-old baby would result in a total family age of 97.5 years, giving an average of 16.25 years, not 16.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.