Question

The present age of father is thrice that of his son's age.Five years from now father's age will be 8 years more than twice of his son's age. Find their present age

Answer 1

$\huge\boxed{\fcolorbox{red}{ink}{Consider:}}$

• Let the present age of the father be a and the present age of the son be b

$\huge\boxed{\fcolorbox{purple}{ink}{GIVEN:}}$

It is given that The present age of father is thrice that of his son's age.

$x−5=3(y−5) \\ \\x−5=3y−15 \\ \\ x−3y=−15+5 \\ \\x−3y=−10 \: \: \: \: \: (1)$

$\huge\fbox\pink{✯Condition✯}$

• Five years from now father's age will be 8 years more than twice of his son's age.

$x+5=2(y+8) \\ \\x+8=2y+16 \\ \\ x−2y=16-5 \\ \\x−2y= 11 \: \: \: \: \: (2)$

$\huge\boxed{\dag\sf\red{NOW}\dag}$

• Subtract equation 1 from equation 2 to eliminate x as the coefficients of x are same

• (x−x)+(−2y+3y)=5+11

i.e. y=16

• place this value of y in (2), we get

x−32=11

i.e. x=11+32=43

$\huge\boxed{\dag\sf\red{Therefore}\dag}$

The present age of the father is 43 years and the present age of the son is 16 years.