Question

Father's age is four times the sum of ages of his two children. After 4 years his age
will be two times the sum of their age. Find the present age of father?​

Answer 1

Answer:

Let the present age of father be ;

x years.

and the sum of ages of his two children be; y years.

Now,

Father's age after 4 years= (x+4) years

And,

Sum of ages of his two children after

4 years = (y + 4 + 4) = (y+8) years

{ after four years, age of both the children will increase by 4 years ,thus

(4+4) ie , 8 years will be increased in the sum of their ages }

Now,

According to the question;

At present, the father's age is 4 times the sum of ages of his two children.

Thus,

=> x = 4y -------(1)

Also,

After 4 years the father's age will be twice the sum of ages of his two children.

Thus,

=> x+4 = 2(y+8)

=> 4y+4 = 2(y+8) {using eq-(1)}

=> 4y + 4 = 2y + 16

=> 4y - 2y = 16 - 4

=> 2y = 12

=> y = 12/2

=> y = 6

Now, using eq-(1), we have;

=> x = 4y

=> x = 4•6

=> x = 24

Hence, the present age of father is;

24 years.

Answer 2

let's suppose father's age =X

and children age=y

after 4 years

father's age = (x+4)

sum of two children's age=(y+8)

we know that

X=4y (1)

and (x+4)=2(y+8)

(X+4)=2y+16

x - 2y =16-4

x-2y. = 12 (2)

by (1),(2)

4y-2y = 12

2y=12/2

y=6

X=4y

X=4×6

X=24

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