Question

Soham‘s father is 3 times as old as Soham. After 10 years his father will be double to Soham‘s age. Find their present ages.

Answer 1

Answer:-

$\sf{The \ present \ ages \ of \ Soham \ and \ his}$

$\sf{father's \ are \ 10 \ and \ 30 \ years \ respectively.}$

Given:

• Soham's father is three times as old as Soham.

• After 10 years his father will be double to Soham's age.

To find:

• Their present ages.

Solution:

$\sf{Let \ the \ Soham's \ age \ be \ x \ years \ and}$

$\sf{his \ father's \ age \ be \ y \ years.}$

$\sf{According \ to \ the \ first \ condition.}$

$\sf{3x=y}$

$\sf{\therefore{3x-y=0...(1)}}$

$\sf{According \ to \ the \ second \ condition.}$

$\sf{2(x+10)=y+10}$

$\sf{\therefore{2x+20=y+10}}$

$\sf{\therefore{2x-y=-10...(2)}}$

$\sf{Subtract \ equation (2) \ from \ equation (1)}$

$\sf{3x-y=0}$

$\sf{-}$

$\sf{2x-y=-10}$

_________________

$\boxed{\sf{x=10}}$

$\sf{Substitute \ x=10 \ in \ equation (1), \ we \ get}$

$\sf{3(10)-y=0}$

$\boxed{\sf{\therefore{y=30}}}$

$\sf\purple{\tt{\therefore{The \ present \ ages \ of \ Soham \ and \ his}}}$

$\sf\purple{\tt{father's \ are \ 10 \ and \ 30 \ years \ respectively.}}$