The average age of 10 members of a family is 29 years. If the youngest members are twins and each is 5 years old, what was the average age (in years) of the family members at the time of birth of the twins?
- A28
- B30
- C31
- D32
Solution & Step-by-step Explanation
Given:
Number of family members currently = 10
Current average age = 29 years
Current total age of the family=10×29=290 years
The twins are currently 5 years old. Therefore, the twins were born 5 years ago.
To find the total age of the family 5 years ago (at the time of birth of the twins), we subtract 5 years from each of the 10 members:
Total age reduction=10×5=50 years
Total age of the family 5 years ago=290−50=240 years
At the time of birth of the twins, they were just born (age 0), but they are excluded from the counting of members to find the average age of the remaining family members, or we count the family before their inclusion. Typically, in such exam problems, "at the time of birth" means we calculate the average age of the remaining 10−2=8 members who were already present.
Number of members excluding twins=10−2=8
Average age of these members=
8
240
=30 years
Number of family members currently = 10
Current average age = 29 years
Current total age of the family=10×29=290 years
The twins are currently 5 years old. Therefore, the twins were born 5 years ago.
To find the total age of the family 5 years ago (at the time of birth of the twins), we subtract 5 years from each of the 10 members:
Total age reduction=10×5=50 years
Total age of the family 5 years ago=290−50=240 years
At the time of birth of the twins, they were just born (age 0), but they are excluded from the counting of members to find the average age of the remaining family members, or we count the family before their inclusion. Typically, in such exam problems, "at the time of birth" means we calculate the average age of the remaining 10−2=8 members who were already present.
Number of members excluding twins=10−2=8
Average age of these members=
8
240
=30 years