A can do a piece of work in 86 days, B can do it in 129 days and C can do the same work alone in 172 days. If on the first day A worked alone and on the second day B and C worked together and on the third day A and C worked together. If they repeat the cycle as follows, then in how many days total work can be completed?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. .
Total work = LCM 86, 129, 172 = 516
Efficiency of A = (516/86) = 6
Efficiency of B = (516/129) = 4
Efficiency of C = (516/172) = 3
Total work per 3-day cycle = 6 + (4 + 3) + (6 + 3) = 22
Total work in 23 cycles (69 days) = 23 × 22 = 506
Remaing work = 516 - 506 = 10
Work done by A on the 70th day = 6
Time to complete the reaming work = (10 - 6)/(4 + 3) = 4/7
Total time required = 70 + (4/7) = days