Solution: A number, here 4p25q is divisible by ‘4’ if the number formed by the last two digits of the number is divisible by 4.

Thus, the number 5q is divisible by 4.This is possible when q = 2(52) or 6(56).

A number, here 4p25q is divisible by ‘9’ if the sum of the digits of the number is divisible by 9.

The sum of the digits = 4 + p + 2 + 5 + q = 11 + p + q. Thus, (11 + p + q) is divisible by 9

If q = 2:

=> 11 + p + q = 11 + p + 2 = 13 + p

13 + p is divisible by ‘9’ when p = 5. (Since, 13 + 5 = 18, which is divisible by 9)

If q = 6:

=> 11 + p + q = 11 + p + 6 = 17 + p

17 + p is divisible by ‘9’ when p = 1. (Since, 17 + 1 = 18, which is divisible by 9)

Therefore, we have two possible combinations:

=> p = 5, q = 2 then \(\frac{p}{q}\) = \(\frac{5}{2}\)

=> p = 1, q = 6 then \(\frac{p}{q}\) = \(\frac{1}{6}\)

Thus, the minimum value of \(\frac{p}{q}\) is \(\frac{1}{6}\).

Therefore, C is the correct answer.

Answer C