Question

Example 9. Father's age is three times
the sum of the ages of his two children. After
5 years, his age will be twice the sum of the
ages of two children. Find the age of father.
[CBSE 2003]​

Answer 1

≡QUESTION≡

Father's age is three times  the sum of the ages of his two children. After  5 years, his age will be twice the sum of the  ages of two children. Find the age of father.

                                                                                   

║⊕ANSWER⊕║

Let the age of father be x years and sum of the ages of his children by y years.

After 5 years,

Father's age = (x + 5) years

Sum of ages of his children = (y + 10) years

From the given information, we have:

x = 3y ...(1)

and

x + 5 = 2(y + 10)

 x - 2y = 15 ...(2)

From (1) and (2), we have,

3y - 2y = 15  y = 15

 x = 3y = 45

∴Father's age = 45 years

                                                                                 

Answer 2

Present age of fathers is       $c =45years$

Step-by-step explanation:

Let present age of two children is  $=a$ years and$=b$ years

     Present age of father is $=c$ years

At present time Father age is three times the sum of ages of two children

$c=3\left ( a+b \right )$

$c/3=\left ( a+b \right )$                          (1)

After 5 years father age will be twice the age of two children.

$c+5=2\left ( a+5+b+5 \right )$

$c+5=2\left ( a+b \right )+20$

$c+5-20=2\left ( a+b \right )$

$c-15=2\left ( a+b \right )$

$c-15=2c\timesc/3$                      (put the value of  (a+b))

$3c-45=2c$

$c =45years$

Present age of father is 45 years