Question

1. The sum of ages of father and son is 64 years. Father says to son, “I am 5 times as old as you were when I was of your age.” What is the sum of digits of son’s age?

Answer 1

son's present age ..... x
father's present age = 64-x

age at which father was the same as son
= 64-x - x = 64-2x
(e.g. suppose the father is now 44 and the son is now 20
the number of years ago, when the father was the same as the son's present age
= 44-20 = 22

64-x = 5(x - (64-2x))
64-x = 5(3x-64)
64-x=15x - 320
-16x = -384
x = 24

the son is now 24 and the father is now 40

editorial: the father was only 16 when his son was born??? MMMMHHHH

check:
son's present age = 24
father's present age = 40
the father had the same age as the son's present age
16 years ago.
at that time the son was 24-16 or 8 years old
which is 5 times as the father's present age