The present age of a father is three times that of his elder son. Four years hence, the age of the father will be four times that of his younger son. If the difference between the present ages of the elder and younger child is 6 years, what is the present age of the father?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 36 years.
Let's consider present age of elder son x and younger son's age y.
Then the father's present age will be 3x.
It is also given that, x – y = 6 ------- equation 1
Now, four years hence:
Age of younger son will be y + 4
Age of father will be 4 (y + 4) = 4y + 16 or 3x + 4
By comparing values:
4y + 16 = 3x + 4
4y + 16 – 4 = 3x
4y + 12 = 3x
(4y + 12) ÷ 3 = x ------- equation 2
Now putting the value of x in equation 1, we get
(4y + 12) ÷ 3 – y = 6
(4y + 12 – 3y) ÷ 3 = 6
4y + 12 – 3y = 6 × 3
4y – 3y = 18 – 12
y = 6 ------- equation 3
By placing the value of y in equation 1, we get:
x – 6 = 6
x = 6 + 6 = 12
Hence, the present of father will be:
3 × 12 = 36
Therefore, the correct answer is 36 years.