Question

A father's age is three times the sum of the ages of his two children. After 5 years his
age will be two times the sum of their ages. Find the present age of father​

Answer 1

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• Father's age is three times the sum of the ages of his two children.
• After five years his age will be two times the sum of their ages.

${\bf{\blue{\underline{Find:}}}}$

• The present age of Father.

${\bf{\blue{\underline{Now:}}}}$

• Let the age of Father be =x
• and the age of his two children be= y

$: \implies{\sf{ x = 3y........(1)}}$

${\bf{\underline{After \:5\:years}}}$

• Age of Father = x+5
• Age of his two children = y+10

$: \implies{\sf{ x + 5= 2(y + 10)}}$

$: \implies{\sf{ x + 5 = 2y + 20}}$

$: \implies{\sf{ x -2y= 20-5}}$

$: \implies{\sf{ x -2y= 15........(2)}}$

__________________________________

Now from (1) and (2),

Put value of x in equation (2),

$: \implies{\sf{ 3y -2y= 15}}$

$: \implies \boxed{\sf{ y= 15 }}$

Now put the value of y in eq (1)

$: \implies {\sf{ x= 3(15) }}$

$: \implies \boxed{\sf{ x= 45 }}$

$\dagger \: \boxed{\sf{ \purple{Hence \: the \: present \: age \: of \: father = 45\:years }}}$

Answer 2

S O L U T I O N :

Let the father's age be r years.

Let the two children's age be m years.

A/q

$\longrightarrow\sf{r=3m..................(1)}$

&

$\underbrace{\bf{After\:5\:years\::}}}}$

The father's age will be (r+5) years.

The two children's will be (m+5+5) years.

So;

$\longrightarrow\sf{(r+5)=2(m+5+5)}\\\\\longrightarrow\sf{r+5=2(m+10)}\\\\\longrightarrow\sf{r+5=2m+20}\\\\\longrightarrow\sf{r-2m=20-5}\\\\\longrightarrow\sf{r-2m=15}\\\\\longrightarrow\sf{3m-2m=15\:\:[from(1)]}\\\\\longrightarrow\bf{m=15\:years}$

Putting the value of m in equation (1), we get;

$\longrightarrow\sf{r=3\times 15}\\\\\longrightarrow\bf{r=45\:years}$

Thus;

$\underbrace{\sf{The\:present\:age\:of\:father's\:will\:be\:r=\boxed{\bf{45\:years}}}}}}$