Answer :
Worker C can complete the work alone in 75 minutes. This is found by subtracting the combined work rate of A and B from the group work rate of A, B, and C. Therefore, it would take C 75 minutes to complete the work alone, so the correct answer is Option B.
The question asks us to determine the time it would take for worker C to complete a piece of work alone, given the time it takes for A, B, and C to complete it together and the time it takes for A and B to complete it together. To solve this, we can use the concept of work rates and the addition of those rates to find the individual rate at which C works.
Let the work to be done be 1 unit. If A, B, and C together complete the work in 30 minutes, their combined work rate is 1/30 work per minute. A and B together take 50 minutes, so their combined rate is 1/50 work per minute. To find C's work rate, we subtract A and B's rate from the group rate:
Work rate of C = (Work rate of A, B, and C) - (Work rate of A and B)
= (1/30) - (1/50) = (5-3)/150 = 2/150
C's work rate is 1/75 work per minute.
