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

$\huge\sf\green{Answer}$

$\boxed{ Answer : 45 \: years }$

$\huge\sf\pink{Explanation :}$

$\sf{Let \:the \:sum\: o f\: the\: age\: of \:two\: children \:be\: x}$

$\sf{So, \:the\: father's \:present \:age\: will \:be \:3x}$

$\sf{5\: years \:later\: sum \:of\: two\: children \:age\: =\: (x + 10)}$

$\sf{Father's \:age \:after \:5 \:years \:=\: 2(x + 10)}$

$\sf{According\: to \:sum,}$

➣3x = 2(x + 10) - 5

➣3x = 2x + 20 - 5

➣3x - 2x = 20 - 5

➣x = 15

$\sf{Father's \:age \:=}$

= 3x

= 3 × 15

= 45

Answer 2

Answer:

The present age of the father is 45 years.

Step-by-step explanation:

Let the present age of father be  'm' and let the sum of present ages of his two children be 'n'.

According to the given situation -

Father's current age = 3 ( the present ages of his two children)

Thus,  m = 3n        ------------- Equation i

After 5 years ...,

Age of father will be  -   (Present age of father)+5

                                      -    =  m+5.

Age of his two children will be = ( Sum of children's present ages) + 10                (Because there are two children)

= n + 10

Accordingly,

Age of father after 5 years = 2 ( Sum of ages of children after 5 years )

m + 5 = 2(n+10)    

m+ 5 = 2n + 20          -------------------------- Equation ii

on solving Equation i and ii

____

Equation i - Eqaution ii

    n = 3m

-    (n+5)= - (2m+20)

m= 15.

Substituting in one of the equation ,

n= 3m

n = 3(15)

n=45

Therfore,

n= 45 and m =15  

_________

This implies that current age of father is 45 years .