Question

Father is now 3 times as old as his son. Four years ago he was four times as old as his son. The present age of the son is?
1) 3 years
2) 4 years
3) 8 years
4)12 years​

Answer 1

Given :

• Father is now 3 times as old as his son.
• Four years ago he was four times as old as his son.

To Find :

• Present Age of his son .

Solution :

$\longmapsto\tt{Let\:Present\:age\:of\:his\:son\:be=x}$

As Given that Father is 3 times as old as his son. So ,

$\longmapsto\tt{Father=3x}$

Before 4 years :

$\longmapsto\tt{Age\:of\:son=x-4}$

$\longmapsto\tt{Age\:of\:father=3x-4}$

A.T Q :

$\longmapsto\tt{3x-4=4(x-4)}$

$\longmapsto\tt{3x-4=4x-16}$

$\longmapsto\tt{3x-4x=-16+4}$

$\longmapsto\tt{-x=-12}$

$\longmapsto\tt\bf{x=12}$

So , The Present Age of his son is 12 years .

Option 4) 12 years is Correct .

Answer 2

AnswEr :

Let's say that , Present age of Father be A years & Present age of Son be B years .

⠀(I) Father is now 3 times as old as his son .

$\\:\implies \sf Father \:=\: 3 \times Son \:$

$:\implies \sf A \:=\: 3 \times B \:$

$:\implies \sf A \:=\: 3B \:\:\qquad \bigg\lgroup \:Eq^n\:(1)\:\bigg\rgroup \:$

» Before 4 Year their ages :

• Father Age will be : ( A - 4 ) years &
• Son Age will be : ( B - 4 ) years .

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

⠀(II) Four years ago he ( Father ) was four times as old as his son .

$\\\longrightarrow \sf Father = \; 4\:(\:Son \:)\:\:$

$\longrightarrow \sf ( A - 4 ) = \; 4\:(\:B - 4 \:)\:\:$

$\longrightarrow \sf ( A - 4 ) = \:(\:4B - 16 \:)\:\:$

$\longrightarrow \sf A - 4\: = \:4B - 16 \:\:$

$\longrightarrow \sf A - 4B\: = \:- 16 + 4 \:\:$

$\longrightarrow \sf \: A - 4B \:=\:-12\:\:\:\qquad \bigg\lgroup \:Eq^n\:(2)\:\bigg\rgroup$

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

☯︎ Substituting , Value of ' A ' from Eq.(1) in Eq.(2) , we get —

$\\\dashrightarrow \sf A - 4B\: = \:-12 \:\:$

$\dashrightarrow \sf 3B - 4B\: = \:-12 \:\:$

$\dashrightarrow \sf - B\: = \:-12 \:\:$

$\dashrightarrow \pmb{\sf B\:=\:12\:}\:$

Therefore,

• Present age of Son , B = 12 yrs &
• Present age of Father , 3B = 3(12) = 36 years .

$\\\:\:\therefore \:\sf \:Hence, \:Present \:age \:of \:Son \:is \:\pmb{\sf Option \:D\:)\:12\:years \:}\:.\:$