Question

Ameen's is one fifth of his father's age. After
6 years his age will be one third of his father
age. How old are they now.​

Answer 1

Step-by-step explanation:

let the Ameen's father's age is x

so ameen's age =x/5

after 6 years father's age=x+6

his age will be x/5+6

by condition that ameen's age will be one third of his father's age

his age =x+6/3

these two equations are equal

x/5+6=x+6/3

x+30/5= x+6/3

3(x+30)=5(x+6)

3x+90=5x+30

90-30=5x-3x

60=2x

30=x

so ameen's age = 30÷5=6

so ammen's age is 6 years and his father's age is 30 years

Answer 2

Given :-

▪ Ameen's age is one fifth of his father's age. After 6 years his age will be one third of his father's age.

To Find :-

▪ Present age of ameen and his father as well.

Solution :-

Let the present age of Ameen's and his father be x and y.

According to the question

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Case 1

☞ Ameen's age is one fifth of his father's age.

⇒ Ameen's age = Father's age / 5

⇒ x = y / 5

⇒ 5x = y ...(1)

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Case 2

☞ After 6 years, Ameen's age will be one third of his father's age.

⇒ Ameen's age + 6 = (Father's age + 6)/3

One would ask why we added 6 to each age, well because the given condition is only true after 6 years.

⇒ x + 6 = (y + 6)/3

⇒ 3x + 18 = y + 6

⇒ 3x + 18 = 5x + 6 [ from (1) ]

⇒ 2x = 12

⇒ x = 6

Substitute [x = 6] in (1), we get

⇒ 5x = y

⇒ 5×6 = y

⇒ y = 30

Hence, The age of Ameen is 6 years and age od his father is 30 years.

Note :-

Always assume present age of persons in age problems.