Question

The ratio of the father's and son's age is 7:4.
The product of their ages is 1008. The ratio
of their ages after 6 years hence will be​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large\underline{\green{\bf Given :-}}$

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• The ratio of the father's and son's age is 7:4

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• The product of their ages is 1008

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$\large\underline{\red{\bf To \: Find :-}}$

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• The ratio of their ages after 6 years

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$\large\underline{\orange{\bf Solution :-}}$

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• Let the present age of father be 7x

• Let the present age of son be 4x

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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$\underline{\bold{\texttt{Father's age :}}}$

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➠ 7x ------ (1)

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$\underline{\bold{\texttt{Son's age :}}}$

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➠ 4x ------ (2)

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The product of their ages is 1008

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➜ 7x × 4x = 1008

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➜ 28x² = 1008

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➜ $\sf x ^2 = \dfrac { 1008 } { 28 }$

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➜ x² = 36

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➜ $\sf x = \sqrt { 36 }$

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• x = 6 ------- (3)
• x = -6

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As age can't be negative hence x = 6

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⟮ Putting x = 6 from (3) to (1) ⟯

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➜ 7x

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➜ 7(6)

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➨ 42

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• Hence father is of 42 years

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⟮ Putting x = 6 from (3) to (2) ⟯

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➜ 4x

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➜ 4(6)

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➨ 24

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• Hence son is of 24 years

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$\underline{\bold{\texttt{Father's age after 6 years :}}}$

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➜ 42 + 6

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➨ 48

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$\underline{\bold{\texttt{Son's age after 6 years :}}}$

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➜ 24 + 6

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➨ 30

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$\underline{\bold{\texttt{Now the ratio of their ages :}}}$

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➜ 48 : 30

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➨ 8 : 5

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Hence the ratio of their ages after 6 years is 8:5

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