A and B together can do a piece of the work in 50 hours, B and C together can do the same work in 75 hours and A and C together can do the same in 25 hours. Find the time in which A, B, and C together will complete the task.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 300/11 hours
A and B can do the work in 50 hours.
B and C can do the work in 75 hours.
A and C can do the work in 25 hours.
Work done is inversely proportional to time taken.
Work done by (A + B) + (B + C) + (A + C) = 2(A + B + C)
The work done by (A + B), (B + C), and (A + C) in an hour is 1/50, 1/75, and 1/25 respectively.
Sum of the work done by (A + B), (B + C), and (A + C) in 1 hour = (1/50) + (1/75) + (1/25)
2(Work done by A + B + C in 1 hour) = Sum of the work done by (A + B), (B + C), and (A + C) in 1 hour
Work done by A + B + C in 1 hour = [(1/50) + (1/75) + (1/25)]/2 = [(3 + 2 + 6)/150]/2 = (11/150)/2 = 11/300
Time in which A, B, and C together will complete the task = 300/11 hours