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

1.	Ameen's is one fifth of his father's age. After 6 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. After 6 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.

▪ Present age of ameen and his father as well.

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.