Question

The father’s age is six times his son’s age. Four years hence, the age of the father
will be four times his son’s age. The present ages, in years, of the son and the
father are, respectively

Answer 1

Answer:

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Answer 2

Question :-

• The father's age is six times his son's age. Four years hence, the age of the father is four times his son's age. Find the present age of the son and his father respectively.

Given :-

• The father's age is six times his son's age.
• Four years hence, the age of the father is four times his son's age.

To Find :-

• What is the present age of son and his father.

Solution :-

Let,

$\begin{gathered}\mapsto \sf\bold{Present\: age\: of\: son\: age =\: x\: years}\\\end{gathered}$

$\begin{gathered}\mapsto \sf\bold{Present\: age\: of\: father\: age =\: 6x\: years}\\\end{gathered}$

After four years :

$\leadsto$ Son age = x + 4 years

$\leadsto$ Father age = 6x + 4 years

According to the question,

$\longrightarrow \sf 6x + 4 =\: 4(x + 4)$

$\longrightarrow\sf 6x + 4 =\: 4(x) + 4(4)$

$\longrightarrow \sf 6x + 4 =\: 4x + 16$

$\longrightarrow \sf 6x - 4x =\: 16 - 4$

$\longrightarrow \sf 2x =\: 12$

$\longrightarrow \sf x =\: \dfrac{\cancel{12}}{\cancel{2}}$

$\longrightarrow \sf x =\: \dfrac{6}{1}$

$\longrightarrow \sf\bold{\purple{x =\: 6\: years}}$

Hence, the required ages of son and his father are :

$\Rightarrow$ Present age of Son :

$\implies \sf x\: years$

$\implies \sf\bold{\red{6\: years}}$

And,

$\Rightarrow$Present age of Father :

$\implies \sf 6x\: years$

$\implies \sf 6(6)\: years$

$\implies \sf 6 \times 6\: years$

$\implies \sf\bold{\red{36\: years}}$

Therefore,

$\begin{gathered}\bigstar \: \: \sf\bold{\green{Present\: age\: of\: son =\: 6\: years}}\\\end{gathered}$

$\begin{gathered}\bigstar \: \: \sf\bold{\green{Present\: age\: of\: Father =\: 36\: years}}\\\end{gathered}$

∴ The present age of son is 6 years and the present age of father is 36 years.

VERIFICATION :

$\to \sf 6x + 4 =\: 4(x + 4)$

$\to \sf 6x + 4 =\: 4x + 16$

By putting x = 6 we get,

$\to \sf 6(6) + 4 =\: 4(6) + 16$

$\to \sf 36 + 4 =\: 24 + 16$

$\to \sf\bold{40 =\: 40}$

Hence, Verified.