# Find The Sum of The Age ?

Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old as his son. Then the sum of the present age of the son and the father is:

1. 108
2. 106
3. 110
4. 105
Anurag Mishra Professor Asked on 23rd September 2015 in

Explanation:-
Let the age of son be X years and the age of his father be Y years.

Eighteen years ago, a father was three times as old as his son.

Then,  3 (X – 18) = Y – 18
3 X – 54 = Y – 18
3 X – Y = 54 – 18
3 X – Y = 36  …………………  (1)

Now, the father is only twice as old as his son.
Then,  2 X = Y
2 X – Y = 0 ………………………….. (2)

Equation (2) is subtracted from edupil equation (1),
3 X – 2 X – Y + Y = 36
X = 36

Put the value of X = 36 in equation (1),
3 x 36  – Y = 36
– Y = 36 – 3 x 36
– Y = – 72
Y = 72

The age of son is X  = 36  years and the age of his father is 72 years.
Then, the sum of the age of son and his father = 36 + 72
= 108 years

Hence, the answer is (1) 108.

Anurag Mishra Professor Answered on 23rd September 2015.