Question

Ben is four times as old as his daughter.

In 20 years’ time Ben shall be twice as old as her.

How old are Ben and his daughter now?

Answer 1

Age of Ben is 40 and age of his daughter ** is **10.

Solution:

Consider Ben’s age be x & his daughters age be y.

So, Ben is four times as old as his daughter.

x = 4y ....(1);

In 20 years’ time Ben shall be twice as old as her.

x+20 = 2(y+20) ....(2);

now, adding x=4y equ(1) in equ(2),

4y+20 = 2y+40;
4y-2y = 40-20;
2y = 20;
y = 10;

So, y=10 adding in equ(1)

x = 4(10);
x = 40;

Answer 2

By the given information we can form 2 equations and hence find the respective ages.

Let Ben’s age be B &

his daughters age be D.

So from the information provided we can write;

B = 4 x D &

B + 20 = 2 x (D + 20)

Substituting B value in the second equation we get.

4D + 20 = 2D + 40

2D = 20

Therefore we get the value of D as;

D = 10

Putting this value in the first equation we get;

B = 4 x D = 4 x 10 = 40′

So Ben’s age is 40

Answer is Ben’s age is 40 and his daughter’s age is 10.

Answer 3

let the age of daughter be =X
Forming equation as 4X+20=(X+20)2
THEN X=10
Hence age be 10 and 40