Question

Two years ago father was three times as old as son and two years hence twice his age will be equal to five times that of his son find their present ages.​

Answer 1

Given

• Two years ago father was three times as old as son.
• Two years hence twice his age will be equal to five times that of his son.

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To find

• Their present ages.

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Solution

• Let the present age of son be x years.

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★ Two years ago

$\tt\longrightarrow{}$ Son's age = x - 2

$\tt\longrightarrow{}$ Father's age = 3(x - 2)

$\tt\longrightarrow{}$ Father's age = 3x - 6

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• Present age of father will be = 3x - 6 + 2
• Present age of father = 3x - 4

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★ Two years hence

$\tt\longrightarrow{}$ Son's age = x + 2

$\tt\longrightarrow{}$ Father's age = 3x - 4 + 2

$\tt\longrightarrow{}$ Father's age = 3x - 2

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⠀⠀⠀⠀⠀According to the question

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$\tt\longmapsto{5(x + 2) = 2(3x - 2)}$

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$\tt\longmapsto{5x + 10 = 6x - 4}$

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$\tt\longmapsto{6x - 5x = 10 + 4}$

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$\bf\longmapsto{x = 14}$

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Hence,

• Present age of son = 14 years
• Present age of father = 3(14) - 4
• Present age of father = 42 - 4
• Present age of father = 38

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