Question

94. A man is 42 years old and his son is 12 years
old. In how many years will the age of the son
be half the age of the man at that time?​

Answer 1

Answer:

18

Step-by-step explanation:

Let the number of years be x.

Therefore the age of son would be 12+x whereas the age of father would be 42+x.

And it is given that the age of father would be twice of the son(same as the age of the son be half of the age of the man), therefore,

2(12+x)=42+x

24+2x=42+x

2x−x=42−24

x=18

Hence, the number of years is 18.

Answer 2

$\bf \: \underline{Given} :$ ↴

$\sf \: Present \: age \: of \: man = 42 \: Years$

$\sf \: Present \: age \: of \: son = 12 \: Years$

$\bf \: \underline{ To \: find }:$ ↴

We have to find the number of years in which the age of the son be half the age of the man.

$\underline{ \bf \: \underline{So, \: Let's \: Start}}$

Let the years after which the son's age becomes the half of the father's be x.

$\sf \: After \: x \: years,$

$\longrightarrow \: \sf \: Son's \: age = (12+x) \: years$

$\sf \longrightarrow \: \: Father's \: age = (42+x) \: years$

$\sf \: \underline{According \: to \: question}$

$\sf \implies \: \dfrac{1}{2} \: (42 + x) = 12 + x$

$\sf \implies \: \dfrac{42}{2} + \dfrac{x}{2} = 12 + x$

$\sf \implies\: 21 + \dfrac{x}{2} = 12 + x$

$\sf \implies \: 21 - 12 = x - \dfrac{x}{2}$

$\sf \implies \: 9 = \dfrac{x}{2}$

$\sf \implies \: x = 9 \times 2$

$\sf \implies \: x= 18$

Hence, after 18 years, the age of son would be the half of the age of father.

$\underline{ \pink{ \boxed{ \sf \: Answer = 18 \: Years }}}$