Answer:
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.
