Question

4 years ago , the father was 6 times as old as his son . ten years later father will be two and a half times as old as his son . determine present of father and his son

Answer 1

Let the present age of son be x.
∴4 years ago son's age = x-4
∴4 years ago the father's age = 6[x-4]
∴After 10 years, son age will be = [x-4+10] = x+6
∴After 10 years, father's age will be = 2 and 1/2 [x+6] = 5/2[x+6]
∴ x-4 + 6[x-4] = x+6 + 5/2 [x+6]
⇒ x-4 + 6x - 24 = x+6 + {5x + 30} /2
⇒7x - 28 = {2x+12+5x+30} /2
⇒2[7x-28] = 7x + 42
⇒14x - 56 = 7x + 42
⇒14x - 7x = 42 + 56
⇒7x = 98
⇒x = 98/7
⇒x = 12.5
∴Son's present age = x = 12.5years = 12 years and 5 months.
∴Father's present age = 10 years after - 10 years before = 5/2[x+6] - 10 = 36.2 years = 36 years and 2 months.

Answer 2

Let the present age of son be x.

∴4 years ago son's age = x-4

∴4 years ago the father's age = 6[x-4]

∴After 10 years, son age will be = [x-4+10] = x+6

∴After 10 years, father's age will be = 2 and 1/2 [x+6] = 5/2[x+6]

∴ x-4 + 6[x-4] = x+6 + 5/2 [x+6]

⇒ x-4 + 6x - 24 = x+6 + {5x + 30} /2

⇒7x - 28 = {2x+12+5x+30} /2

⇒2[7x-28] = 7x + 42

⇒14x - 56 = 7x + 42

⇒14x - 7x = 42 + 56

⇒7x = 98

⇒x = 98/7

⇒x = 12.5

∴Son's present age = x = 12.5years = 12 years and 5 months.

∴Father's present age = 10 years after - 10 years before = 5/2[x+6] - 10 = 36.2 years = 36 years and 2 months.