Explanation:

the sum of the three numbers should leave a remainder 43 + 47 + 49 = 139.
Or, it should be of the form N * k + 139, where K is an integer.
However, it leaves a remainder 9, or it is of the form N * m + 9.
N * k + 139 = N * m + 9
N * (m - k) = 130
Or, N should be a factor of 130.
Since the remainders left on division by N are 43, 47 and 49, N should be greater than 49.
The only factors of 130 that are greater than 49 are 65 and 130.
So, N can take 2 values – 65 or 130.