Ameen's is one fifth of his father's age. After6 years his age will be

1.	Ameen's is one fifth of his father's age. After6 years his age will be one third of his fatherage. How old are they now.
Answer» 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 ▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 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) ▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ 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.

Ameen's is one fifth of his father's age. After6 years his age will be one third of his fatherage. How old are they now.

Answer»

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.