The average age of 5 members is 21 years. If the age of the youngest member is 5 years, then what was the average age of the family at the birth of the youngest member?
Answer: C
Current total age of 5 members = 5 × 21 = 105 years.
5 years ago, the sum of their ages would have been 105 - (5 members × 5 years) = 105 - 25 = 80 years.
At the birth of the youngest member (5 years ago), there were only 4 members in the family (the youngest was just born, age 0).
Average age at that time = Total sum of ages of the 4 members / 4. This is tricky. The sum of ages of the 4 older members 5 years ago was 80. The average age was 80/4 = 20 years. Let's re-verify. Let ages be a,b,c,d,e. (a+b+c+d+e)/5 = 21. Sum = 105. Youngest e=5. At birth of e, ages were a-5, b-5, c-5, d-5. The sum of their ages was (a+b+c+d)-20. We know a+b+c+d = 105-5=100. So sum was 100-20=80. Average = 80/4 = 20.