Question

Ajay is four times as old as his son After 16 years he will be twice as old as his son find his son's present age​

Answer 1

$\bf\huge\underline{Answer :-}$

The present age of the son is 8 years

$\huge{\mathfrak{\underline{Explanation :-}}}$

Given :

•Age of Ajay = Four times the age of his son.

•After 16 years, Ajay will be twice the age of his son.

To find :

The present age of Ajay's son

Solution :

Let the age of Ajay's son be 'x' yrs

and the age of Ajay be '4x' yrs

After 16 years,

Age of his son = (x + 16) yrs

Age of Ajay = (4x + 16) yrs

According to question,

$\sf\longrightarrow 4x + 16 = 2(x + 16)$

$\sf\longrightarrow 4x + 16 = 2x + 32$

$\sf\longrightarrow 4x - 2x = 32 - 16$

$\sf\longrightarrow 2x = 16$

$\sf\longrightarrow x = \dfrac{16}{2}$

$\sf\therefore x = 8$

Hence, the age of Ajay's son is 8 years respectively.

Answer 2

$\bold{\underline{\underline{\huge{\sf{AnsWer:}}}}}$

Present age of son = 8 years

$\bold{\underline{\underline{\large{\sf{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• Ajay is four times as old as his son
• After 16 years he will be twice as old as his son

To FiNd :

• Present age of Son

SoLuTiOn :

Let the present age of Ajay be 4x years.

Let the present age of Son x years.

$\sf{\underline{\underline{As\:PeR\:tHe\:QuEsTiOn:}}}$

• After 16 years he will be twice as old as his son .

AgE aFtEr 16 yEaRs :

• Ajay = 4x + 16 years
• Son = x + 16 years

Constituting it mathematically,

$\hookrightarrow$ $\sf{4x\:+\:16\:=\:2\:(x\:+\:16)}$

$\hookrightarrow$ $\sf{4x\:+\:16\:=\:2x\:+\:32}$

$\hookrightarrow$ $\sf{4x\:-\:2x\:=\:32\:-\:16}$

$\hookrightarrow$$\sf{2x\:=\:16}$

$\hookrightarrow$ $\sf{x\:=\:{\dfrac{16}{2}}}$

$\hookrightarrow$ $\sf{x\:=\:8}$

•°• Present age of Son = 8 years

$\bold{\huge{\boxed{\sf{\red{VeRiFiCaTiOn:}}}}}$

Age after 16 years :

Son :

$\hookrightarrow$ $\sf{x\:+\:16}$

$\hookrightarrow$ $\sf{8\:+\:16}$

$\hookrightarrow$ $\sf{24}$

Age of Son = 24 years

Ajay :

$\hookrightarrow$ $\sf{4x\:+\:16}$

$\hookrightarrow$ $\sf{4\:\times\:8\:+\:16}$

$\hookrightarrow$ $\sf{32\:+\:16}$

$\hookrightarrow$ $\sf{48}$

•°• Age of Ajay = 48 years

Given :

• Ajay will be twice as old as his son after 16 years.

$\hookrightarrow$ $\sf{4x\:+\:16\:=\:x\:+\:16}$

After solving, 4x + 16 we got the result 48 and for x + 16 we got 24, substituting the appropriate values,

$\hookrightarrow$ $\sf{48\:=\:2(24)}$

$\hookrightarrow$ $\sf{48\:=\:48}$

LHS = RHS

Hence substantiated.