Question

29) The father's age is six times his son's age Four years hence, the age of the fat
four times his son's age The present ages of the son and the father are, respectiv
​

Answer 1

Given that, Age of father is six times age of his son. Four years hence or after four years, The age of father will be four times his son's age.

❍ So, Let's consider age of his son be x years.

⠀ ⠀Therefore, age of father will be 6x years.

⠀━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

☆ After four years,

• Age of Son = (x + 4) years
• Age of father = (6x + 4) years

⠀⠀⠀

$\qquad\bigstar\:{\underline{\pmb{\frak{\pink{According~to~the~Question~:}}}}}\\\\\\ \qquad\dashrightarrow\sf Father's\:age = 4 \bigg(Son's\:age \bigg)\\\\\\ \qquad\dashrightarrow\sf 6x + 4 = 4 \bigg(x + 4 \bigg)\\\\\\ \qquad\dashrightarrow\sf 6x + 4 = 4x + 16\\\\\\ \qquad\dashrightarrow\sf 6x - 4x = 16 - 4\\\\\\ \qquad\dashrightarrow\sf 2x = 12\\\\\\ \qquad\dashrightarrow\sf x = \cancel{\dfrac{12}{2}}\\\\\\ \qquad\dashrightarrow{\underline{\boxed{\pmb{\frak{x = 6}}}}}\:\bigstar$

Therefore,

⠀⠀⠀

• Age of Son, x = 6 years
• Age of his father = 36 years

⠀⠀⠀

$\therefore\:{\underline{\sf{Hence,\:Present\:Age\:of\:father\:\&\:his\:son\:is\:{\pmb{36\:\sf{and}\:6\:years}}\:\sf{respectively.}}}}$

Answer 2

Answer:

Appropriate 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,

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

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

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,

$\bigstar \: \: \sf\bold{\green{Present\: age\: of\: Son =\: 6\: years}}$

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

$\therefore$ The present age of son is 6 years and the present age of father is 36 years.

$\rule{150}{2}$

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.