A', 'B' and 'C' can complete a piece of work in 28 days, 32 days and 42 days respectively. 'D' is as efficient as 'A' and 'C' together. Only one person can do the work on any
day, so they take daily turns to do the work. On the first day 'C' does the work, followed by 'D', 'A' and 'B' on subsequent days; repeating this until the work is completed. In
how many days will the work be completed?
Answers
Answer:
A starts the work and does 1/16 of the work on the first day
B works on the 2nd day and does 1/12 of the work
Thus in two days both of them would complete 1/16 + 1/12 of the work i.e. 4+3/48 (48 being the L.C.M of 16 and 12). In two days they finish 7/48 of the work.
In 6 cycles (A on 1st day + B the next day) they would complete 6 x 7 = 42/48 of the work. Now only 6 units of work remains to be done.
The remaining work is 6/48. On the 13th day, A comes and does 1/16 of the whole work which is 1/16 of 48, i.e., 3 units of the work and only 3 units of work is still remaining. B comes the next day i.e. on the 14th day and 1/12 of 48 i.e. 1/12 *48 which is 4 units. But only 3 units of work is required to be completed on the 14th day and B takes 3/4 of the day to complete the 3 remaining units of work
Thus the total time taken by both of them is 13 and 3/4 days.
Step-by-step explanation: