$$x^2-2px+m=0$$
m is divisible by 5 and less 102 and has root as 7
$$7^2-2p\left(7\right)+m=0$$
$$49-14p+m=0$$
m = 14p - 49
Since m is divisible by 5, 14p - 49 is a multiple of 5. Also, since p is a prime number, the only prime that can make m divisible by 5 and less than 120 is 11
Therefore, m = 14 (11) - 49
m = 154 - 49 = 105
$$For\ x^2-2px+n=0$$
root is 12
$$12^2-2p\left(12\right)+n=0\ \ \ where\ p=11$$
$$144-2\left(11\right)\left(12\right)+n=0$$
144 - 264 + n = 0
n = 120

Therefore, p + n - m = 11 + 120 - 105 = 26
Answer = option D