The correct answer is (c).
A can do a work in 5 days, B can do the same work in 10 days and C can do it in 30 days. If A, B and C work together, then the amount of work they can do in one day is:
A + B + C = 1/5 + 1/10 + 1/30 = 11/60
Therefore, A, B and C can complete the work in 60/11 days, which is approximately 5.45 days. Since the question asks for the number of days required to complete the work, the answer is (c).
Option (a) is incorrect because it is the number of days required for A to complete the work alone. Option (b) is incorrect because it is the number of days required for B to complete the work alone. Option (d) is incorrect because it is the number of days required for C to complete the work alone.