Question

A man is thrice as old as his son . five year ago the man was four times as old as his son . Find their present ages
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Answer 1

Answer :-

Let the present ages of Son and his father are x and y respectively

then, according to the question ;(A man is thrice as old as his son)

• y = 3x ....(i)

five year ago,

• age of man = y - 5
• age of his son = x - 5

and according to the question,(Five years ago the man was four times as old as his son)

• (y - 5) = 4(x - 5)

➪ y - 5 = 4x - 20

➪ y - 5 - 4x + 20 = 0

➪ y - 4x + 15 = 0

• y + 15 - 4x = 0 ....(ii)

now, we have two equations

• y = 3x ....(i)
• y + 15 - 4x = 0 ....(ii)

now, substitute the value of y from (i) in (ii)

$\bold{: \implies 3x + 15 - 4x = 0} \\ \\ \bold{ : \implies 3x - 4x = - 15 }\: \: \: \: \\ \\ \bold{: \implies \cancel - x = \cancel - 15} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies x = 15} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so,the present age of his son is 15 years

then, present age of the man = 3 × 15 = 45 years

hence,

the age of son is 15 years and age of the man is 45 years

Answer 2

A n s w e r

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G i v e n

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• A man is thrice as old as his son

• Five years ago the man was four times as old as his son

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F i n d

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• Their present ages

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S o l u t i o n

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• Let the present age of the man be 'm'

• Let the present age of the son be 's'

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Given that , the man is thrice as old as his son

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Thus ,

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: ➜ m = 3s ⚊⚊⚊⚊ ⓵

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$\underline{ \underline{\bold{\texttt{Five years ago man's age :}}}}$

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➠ m - 5

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$\underline{ \underline{\bold{\texttt{Five years ago son's age :}}}}$

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➠ s - 5

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Also given that , five years ago the man was four times as old as his son

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Thus ,

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: ➜ (m - 5) = 4(s - 5)

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: ➜ m - 5 = 4s - 20

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: ➜ m - 4s = -20 + 5

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: ➜ m - 4s = - 15 ⚊⚊⚊⚊ ⓶

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⟮ Putting m = 3s from ⓵ to ⓶ ⟯

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: ➜ m - 4s = - 15

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: ➜ 3s - 4s = - 15

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: ➜ -1s = - 15

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: : ➨ s = 15 ⚊⚊⚊⚊ ⓷

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• Hence the present age of son is 15 years

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⟮ Putting s = 15 from ⓷ to ⓵ ⟯

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: ➜ m = 3s

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: ➜ m = 3(15)

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: : ➨ m = 45

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• Hence the present age of the man is 45 years

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∴ The present ages of the man and his son are 45 years & 15 years respectively