Question

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

Answer 1

AnswEr :

$\bf{\large{\underline{\rm{Given\::}}}}$

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

$\bf{\large{\underline{\rm{To\:find\::}}}}$

The present age of the father.

$\bf{\large{\underline{\tt{\red{Explanation\::}}}}}$

Let the present age of the father's be R years.

Let the present age of sum his two children be M years.

$\bf{\large{\underline{\underline{\tt{\orange{A.T.Q\::}}}}}}}$

$\leadsto\rm{R\:=\:3M.............................(1)}$

$\bf{\large{\boxed{\sf{After\:5\:yearS\::}}}}}}$

$\bullet\sf{Father\:age\:=\:(R+5)\:years}\\\\\bullet\sf{Sum\:of\:two\:children\:age\:=\:(M+5+5)\:years}$

So,

$\longrightarrow\tt{(R+5)=2(M+5+5)}\\\\\\\\\longrightarrow\tt{R+5=2(M+10)}\\\\\\\\\longrightarrow\tt{R+5=2M+20}\\\\\\\\\longrightarrow\tt{R=2M+20-5}\\\\\\\\\longrightarrow\tt{R\:=\:2M+15}\\\\\\\\\longrightarrow\tt{3M=2M+15\:\:\:\:\:\:\:\:\:\:\big[From\:(1)\big]}\\\\\\\\\longrightarrow\tt{3M-2M=15}\\\\\\\\\longrightarrow\tt{\red{M\:=\:15\:years}}$

Hence,

The present age of the father's = 3(15) years.

The present age of the father's = 45 years.

Answer 2

AnsweR :-

Given:

• The sum of ages of two children = Father's age
• After 5 years, two times the sum of their ages = Father's age

To find:

• Present age of the father

Solution:

Let the sum of the present ages of his children = S.

And let the present age of the father be = F.

Now, in situation 1,

➜ F = 3 ( M )...(1)

And in situation 2,

➜ F + 5 = 2 ( M + 10 )

➜ F = 2M + 20 - 5

➜ F = 2M + 15...(2)

Now, both the questions we got are equal to F.

So,

➜ F = 2M + 15 = 3M

➜ 2M + 15 = 3M

➜ M = 15 years

Now, we got that the sum of present ages of his two children is 15.

So, using the first equation,

➜ F = 3 ( M )

➜ F = 3 ( 15 )

➜ F = 45 years.

So, the present age of the father is 45 years.

$\rule{200}2$