Question

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

Answer 1

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

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

$\underline{\pink{ 6 \: years \: ago : }}$

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

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

/* 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.,

$\red{ Present \:age \: of \: Son } \green { = 21 \: years }$

$\red{ Present \:age \: of \: Father}\\= x + 30 \\= 21 + 30\\ \green { = 51 \: years }$

•••♪

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 the age of son be x and the age of father = (x + 30)

6 years ago -

Their ages -

• Son's age = x - 6
• Father's age = (x + 30 - 6) = (x + 24)

According to the question,

↬ x + 24 = 3(x - 6)

↬ x + 24 = 3x - 18

↬ 24 + 18 = 3x - x

↬ 48 = 2x

↬ 21 = x

• The value of x = 21

Their present ages -

• Son's age = x = 21 years
• Father's age = x + 30 = 21 + 30 = 51 years

━━━━━━━━━━━━━━━━━━━