John is eight year older than his sister.In three years,he will be as twice as she will be then.

Question

How old are they both now?

Answer 1

J = John present age

S = sister present age

J = S + 8

After 3 years John wil be J + 3 yrs old.

Sister wil be S + 3 yrs old.

In three years,he will be as twice as she will be then mean:

( J + 3 ) / ( S + 3 ) = 2

In this equation replace J with S + 8

( S + 8 + 3 ) / ( S + 3 ) = 2

( S + 11 ) / ( S + 3 ) = 2

Multiply both sides by S + 3

S + 11 = 2 ( S + 3 )

S + 11 = 2 S + 6

Subtract 6 to both sides

S + 11 - 6 = 2 S + 6 - 6

S + 5 = 2 S

Subtract S to both sides

S + 5 - S = 2 S - S

5 = S

S = 5

J = S + 8 = 5 + 8 = 13

John is 13 yrs old, sister is 5 yrs old.

Proof:

After 3 years John wil be 13 + 3 = 16 yrs old

Sister wil be 5 + 3 = 8 yrs old

16 / 8 = 2

Answer 2

Sister: X yrs. old.
John: x + 8 yrs. old.

3 yrs. later:
Sister: x + 3.
John: (x+8) + 3 = x + 11.
x + 11 = 2(x + 3),
X = 5.
x + 8 = 5 + 8 = 13.