Five years ago, A was three times as old as B and ten years later, A shall be twice as old as B. What are the present ages of A and B (in years).

Answer 1

50,20

Answer 2

A = Present age of A

B = Present age of B

Five years ago person A was A - 5 yrs old.

Person B was B - 5 yrs old.

Five years ago, A was three times as old as B mean:

A - 5 = 3 ( B - 5 )

Ten years later person A shal be:

A - 5 + 10 = A + 5 yrs old

Person B shal be:

B - 5 + 10 = B + 5 yrs old

Ten years later, A shall be twice as old as B mean:

A + 5 = 2 ( B + 5 )

Now you must solve system:

A - 5 = 3 ( B - 5 )

A + 5 = 2 ( B + 5 )

A - 5 = 3 * B - 3 * 5

A - 5 = 3 B - 15

A + 5 = 2 ( B + 5 )

A + 5 = 2 * B + 2 * 5

A + 5 = 2 B + 10

Your system become:

A - 5 = 3 B - 15

A + 5 = 2 B + 10

Try to solve this system.

The solutions are: A = 35 , B = 15

Proof:

Five years ago person A was 35 - 5 = 30 yrs old.

Five years ago person B was 15 - 5 = 10 yrs old.

30 / 10 = 3

Ten years later person A shal be:

30 + 10 = 40 yrs old

Person B shal be:

10 + 10 = 20 yrs old

40 / 20 = 2