Mother's Age

Let average age of family at marriage time = x then sum of ages = 7x

after death after 12 years total of ages of family = (7(x + 12) – m + 0) where m is mothers age and 0 is age of newly born

now average = [7(x + 12) – m]/7 = x solving m = 84

Let the average age of family members at the time of marriage be x

Sum of the ages of the family members at that time is 7x --> eq 1

After 12 years (i.e. now) the ages of all the seven would have increased by 12 each i.e by 84 years (12 X 7)

Hence total ages of all the members currently = 7x + 84

Now mother has died and new baby is born. New baby's age now is zero.

Hence, mother's age should be subtracted from the current total. Also the baby's age should be added to the total.

Current age total all the members = 7x + 84 - mother's age + baby's age = 7x + 84 - mother's age (since baby's age is zero) --> eq 2

But the question says that the average now has become same as that of 12 years before.

Hence 7x + 84 - mother's age = 7x

Hence mother’s age is 84 years.