Question

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

​

Answer 1

let father's age be x

and sum of children's age be y

x=3y

x+5=2(y+5)

3y+5=2y +10

y=5

Answer 2

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$\bold{\Huge\red{\boxed{{{Answer}}}}}$

✒ Age is father is 45 years

$\bold{\Huge\blue{\boxed{{{Given}}}}}$

✒ Father's age is three times the sum of ages of his two children.

✒ After 5 years, his age will be twice the sum of ages of two children.

$\bold{\Huge\pink{\boxed{{{To\: Find}}}}}$

✒ Age of Father = ?

$\bold{\huge\green{\boxed{{{Explanation}}}}}$

✏ let the age of father to be 'x' year.

✏ let the age of his 2 sons to be 'y' year.

So,

$\boxed{=> x = 3y .........(1)}$

⭐ Now, A.T.Q (After 5 years, his age will be twice the sum of ages of two children.)

✏ Age of father

$\boxed {\bold{= (x + 5) \: years}}$

✏ Sum of age of his two sons

$\boxed{ \bold{= [y + 2(5)] }}$

$\boxed{ \bold{= (y + 10) years}}$

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⭐ Now Again, A.T.Q (After 5 years, his age will be twice the sum of ages of two children.)

$\boxed{=> x + 5 = 2}$

$\boxed{=> x + 5 = 2y + 20}$

$\boxed{=> x - 2y = 15 .............(2)}$

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⭐ From equation (1) and (2)

✏ Putting the value of equation (1) and (2) we get,

$\boxed{=> 3y - 2y = 15}$

$\boxed{=> y = 15 }$

✏ Putting the value of (y = 15) equation (1) we get,

$\boxed{=> x = 3(15)}$

$\boxed{=> x = 45}$

Hence, the age of father is 45 years.

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