Question

Four years ago the father was three times as old as the son. The sum of their present ages is 72 years. The present age of the father is ?​

Answer 1

~Answer :

• Present age of Father is 52 years.

Given : Four years ago the father was three times as old as the son. The sum of their present ages is 72 years.

To Find : The Present age of the Father ?

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Solution : Let the Present age of Father be 'x'.

$~$

• Four years ago the Father was three times as old as the son.

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• Son's age = x
• Father's age = 3x

$~$

• Sum of their Present ages of 72 years.

$~$

~Present ages,

• Son's age = x + 4
• Father's age = 3x + 4

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${\bf{\underline{\pmb{According~to~the~given~Question~:}}}}$

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${\sf:\implies{(x~+~4)~+~(3x~+~4)~=~72}}$

${\sf:\implies{x~+~3x~+~4~+~4~=~72}}$

${\sf:\implies{4x~+~8~=~72}}$

${\sf:\implies{4x~=~72~-~8}}$

${\sf:\implies{4x~=~64}}$

${\sf:\implies{x~=~\cancel\dfrac{64}{4}}}$

• ${\underline{\boxed{\pmb{\sf{\pink{x~=~16}}}}}} \; {\red{\bigstar}}$

$~$

Therefore,

• Present age of Son = x + 4
• Present age of Son = 16 + 4 = 20 years
• Present age of Father = 3x + 4
• Present age of Father = 48 + 4 = 52 years.

$~$

Hence,

• Present age of Father is 52 years.