Question

A father is 30 years older than his son. Six years ago the father was 3 times as old as his son. How old is the father and son

Answer 1

Let age of son be x

So, father's age will be 30+x

6 Year ago,

3{6-(30+x)}=x

3{180+6x}=x

540+18x=x

x=31

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Answer 2

⛦Given -

• A father is 30 years older than his son.
• Six yrs ago the father was 3 times as old as his son.

⛦To find -

• Present ages of father and son.

⛦Solution -

$Let \:Present \:age \: of \: son = x \: years$

$Present \:age \: of \: Father = ( x + 30) \: years$

6 years ago.....

$Age \: of\: son = ( x - 6 ) \: years$

$Age \: of \: father = ( x + 30 - 6 ) \\= ( x + 24 ) \: years$

According to the problem given

$Father's \: age = 3 \times ( son's \: age )$

$\implies x + 24 = 3( x - 6)$

$\implies x + 24 = 3x - 18$

$\implies 24 + 18 = 3x - x$

$\implies 42 = 2x$

$\implies \frac{42}{2} = x$

$\implies x = 21$

↬Therefore.,

• Present age of Son = 21 years
• Present age of Father = x + 30 = 21 + 30 = 51 years

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