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?

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

To find the sum of the digits of the son's age, we need to first setup and solve the given problem.

Let's assume the son's age is "x" years. According to the given information, the father's age would be (64 - x) years.

The father says, "I am 5 times as old as you were when I was of your age." This statement implies that the son's age (x years ago) was equal to the father's age when he was x years old.

So, we can set up the equation:

x = 5 * (64 - x)

Now, let's solve this equation to find the value of x:

x = 320 - 5x
6x = 320
x = 320/6
x = 53.33 (approx.)

Since age cannot be in decimal form, we can conclude that the son's age is approximately 53 years.

Now, to find the sum of the digits of the son's age, we add the individual digits:

Sum of digits = 5 + 3 = 8

Therefore, the sum of the digits of the son's age is 8.