N and p stand for two numbers

N is a multiple of 5

P is a multiple of 6

N/p = 2/3

N=?

P=?

There are infinite pairsof numbers (N, P) that are solution. For example: (20,30), (40, 60), (30,90)

Explanation:

1) Being N a multiple of 5, it can be 5, 10, 15, 20, 25, ...

2) Being P a multiple of 6 it can be 6, 12, 18, 24, 30, ...

3) N / P = 2/3 = > 3N = 2P

4) The possible values of N and 2N are:

N 3N

5 6

10 30

15 45

20 60

25 75

And so on.

...

5) The possible values of P and 2P are:

P 2P

6 12

12 24

18 36

24 48

30 60

36 72

6) So, N is 20, and P = 30 is a solution, because 20 is multiple of 5, 30 is multiple of 6, and 20/30 = 2/3.

Is that the only solution?

No, it isnt. Some multiples of 20 and 30 meet all the conditions:

For example, N = 40 is multiple of 5, P = 60 is multiple of 6 and 40 / 60 = 2/3

Other example: N = 60 is multiple of 5, 90 is multople of 6 and 60/90 = 2/3.

This is the sequence of pair N, P that meet the conditions:

N P

20 30

40 60

60 90

80 120

100 150

And so on.