# Four years hence, the age of the gather will be four times his son’s age

The father’ age is six times his son’s age. Four years hence, the age of the gather will be four times his son’s age. The present age, in years, of the son and the father are, respectively
(a) 4 and 24
(b) 5 and 30
(c) 6 and 36
(d) 7 and 42

Anurag Mishra Professor Asked on 29th February 2016 in

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

The father’s age is six times his son’s age,
Then,  X = 6 Y
X – 6 Y = 0 ………………………. (1)

Four years hence, the age of the gather will be four times his son’s age.
Then,   X + 4 = 4 (Y + 4)
X + 4 = 4 Y + 16
X – 4 Y = 16 – 4
X – 4 Y = 12 …………………….(2)

Equation (2) Subtract from equation (1),
X – 6 Y – X + 4 Y = 0 – 12
– 2 Y = -12
2 Y = 12
Y = 12/2
Y = 6

Then, the age of Son is Y  = 6 years and age  of his father = X = 6 Y = 6 x 6 => 36 years.

Hence, the correct answer is option (c) 6 and 36 years.

Anurag Mishra Professor Answered on 4th March 2016.