Question

The age of the father and son is in the ratio 4:1 . After 5 years their age will be in ratio of 3:1 . Find their present ages.

Answer 1

➲ Let: The ratio of their ages be x.

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Then,

→ Present age of father = 4x

→ Present age of son = x

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After 5 years,

→ Age of father = 4x + 5

→ Age of son = x + 5

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It is given that,

After 5 years their age will be in ratio of 3:1.

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According to the question

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$\tt\longrightarrow{\dfrac{4x + 5}{x + 5} = \dfrac{3}{1}}$

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$\tt\longrightarrow{4x + 5 = 3(x + 5)}$

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$\tt\longrightarrow{4x + 5 = 3x + 15}$

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$\tt\longrightarrow{4x - 3x = 15 - 5}$

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$\tt\longrightarrow{x = 10}$

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By putting the value of x

→ Present age of father = 4x = 40 years

→ Present age of son = x = 10 years.

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Hence,

• Present age of father and son is 40 and 10 years respectively.

Answer 2

Step-by-step explanation:

Given: The age of the father and son is in the ratio of 4 : 1. After 5 years their age will be in ratio of 3 : 1.

Need to find: Present ages ?

❏ Let the common ratio of their ages be x.

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__________________

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$\frak{\underline{\underline{\dag Present\ ages\ :-}}}$

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$\bf {Here} \begin{cases} &\sf{Father's\ age\ =\ 4x.} \\ &\sf{Son's\ age\ =\ x.} \end{cases}$

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$\frak{\underline{\underline{\dag After\ 5\ years,\ we\ know\ that\ :-}}}$

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$\bf {Here} \begin{cases} &\sf{Father's\ age\ =\ 4x\ +\ 5.} \\ &\sf{Son's\ age\ =\ x\ +\ 5.} \end{cases}$

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❏ Since, it is given that after 5 years the ratio of their ages will be 3 : 1.

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$\boldsymbol{\underline{\bigstar According\ to\ the\ question\ :-}}$

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$\sf : \implies {\dfrac{4x\ +\ 5}{x\ +\ 5}\ =\ \dfrac{3}{1}} \\ \\ \\ \sf : \implies {4x\ +\ 5\ =\ 3(x\ +\ 5)} \\ \\ \\ \sf : \implies {4x\ +\ 5\ =\ 3x\ +\ 15} \\ \\ \\ \sf : \implies {4x\ -\ 3x\ =\ 15\ -\ 5} \\ \\ \\ \sf : \implies {\underline{\boxed{\purple{\bf x\ =\ 10.}}}}\bigstar$

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Therefore,

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• Father's age = 4x = 4 × 10 = 40 years.
• Son's age = x = 10 years.

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$\sf \therefore {\underline{Hence,\ the\ present\ age\ of\ father\ is\ \bf 40\ years\ \sf and\ son\ age\ is\ \bf 10\ years.}}$