Question

The sum of the ages of father and his son is 84 years. When the father was as old
as his son now, he was five times as old as his son. Find their present ages.​

Answer 1

Step-by-step explanation:

Let the present age of son be x.

Then, present age of father is (60−x).

According to the question,

⇒ (60−x)−6=5(x−6)

⇒ 54−x=5x−30

⇒ 54+30=5x+x

⇒ 84=6x

⇒ x=

6

84

⇒ x=14

∴ Son's age after 6 years =(x+6)years

=(14+6)years

20 yrs

Answer 2

The father is 54 while the son is 30.

When doing this question, the key thing to remember is that the absolute difference in age (father’s age - son’s age) is constant. So from the second statement we:

↬let age of the younger son be x,

↦ Son’s present age / younger father

↦ = 5x

↦ Difference in age = 4x

↦Therefore 84 = son’s present age +

-- (son’s present age + age difference)

↦= 5x + 9x

↬Thus x = 84/14 = 6

↦Son’s age = 5x =30 and father’s age

↦= 9x = 54