A, B and C can do a work seperately in 18, 36 and 54 days, respectively. They started the work together, but B and C left 5 days and 10 days, respectively, before the completion of the work. In how many days was the work finished?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 13 days.
Please note that, If someone left the work before the completion of the work then to ease problem-solving one should add the work done by them in these days to the total work.
Total work = LCM of 18, 36 and 54 = 108 units.
Efficiency of A = 108/18 = 6 units/day
Efficiency of B = 108/36 = 3 units/day.
Efficiency of C = 108/54 = 2 units/day.
Work done by B in 5 days = 5 × 3 = 15 units.
Work done by C in 10 days = 10 × 2 = 20 units.
Total time taken by all of them to complete the work = total work/ total efficiency.
= (108 + 15 + 20)/(6 + 3 + 2) = 143/11 = 13 days.