Question

10.A man's age is three times his son's age.Ten years ago he was five times his son's age. Find their present age.​

Answer 1

Given :

• Aman's age is 3 times his son's age.
• Then years ago Aman was five times his son's age.

To Find :

• Present age of Aman and his son.

Solution :

$\longrightarrow\tt{Let\:the\:age\:of\:son\:be=x}$

As Given that Aman's age is 3 times of his son's age.So ,

$\longrightarrow\tt{Age\:of\:Aman=3x}$

Ten Years Ago :

$\longrightarrow\tt{Age\:of\:his\:son=x-10}$

$\longrightarrow\tt{Age\:of\:Aman=3x-10}$

A.T.Q :

$\longrightarrow\tt{5(x-10)=3x-10}$

$\longrightarrow\tt{5x-50=3x-10}$

$\longrightarrow\tt{5x-3x=-10+50}$

$\longrightarrow\tt{2x=40}$

$\longrightarrow\tt{x=\cancel\dfrac{40}{2}}$

$\longrightarrow\tt\bold{x=20}$

Therefore :

$\longrightarrow\tt{Present\:age\:of\:son=x}$

$\longrightarrow\tt\boxed{20\:yrs}$

$\longrightarrow\tt{Present\:age\:of\:Aman\:age=3x}$

$\longrightarrow\tt{3(20)}$

$\longrightarrow\tt\boxed{60\:yrs}$