P, Q, R and S can complete a piece of work in 25 days, 30 days, 36 days and 40 days, respectively. They work on a rotation basis with Q working on the first day, S on the second day, P on the third day and R on the fourth day, then again Q on the fifth day and so on. In how much time will the work be completed?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. days
Total work = LCM(25,30,36,40) = 1800 units.
Q's efficiency = 1800 ÷ 30 = 60 units per day.
S's efficiency = 1800 ÷ 40 = 45 units per day.
P's efficiency = 1800 ÷ 25 = 72 units per day.
R's efficiency = 1800 ÷ 36 = 50 units per day.
Work in one 4-day cycle = 60 + 45 + 72 + 50 = 227 units.
Number of full 4-day cycles = 1800 ÷ 227 = 7.92 = 7 cycles.
Days for 7 cycles = 7 × 4 = 28 days.
Work done in 7 cycles = 7 × 227 = 1589 units.
Remaining work = 1800 − 1589 = 211 units.
Day 29 (Q) does 60 units; remaining = 211 − 60 = 151 units.
Day 30 (S) does 45 units; remaining = 151 − 45 = 106 units.
Day 31 (P) does 72 units; remaining = 106 − 72 = 34 units.
R's efficiency = 50 units per day, fraction of R-day needed = 34 ÷ 50 = 17/25 day.
Total time = 31 + 17/25 days = days.