Parth, Rizwan and Sangeeta can do a piece of work in 40, 60 and 80 days, respectively. In how many days can Parth do the work if he is assisted by Rizwan and Sangeeta on every third day?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 29.
Parth 1 day work = 1/40
Rizwan 1 day work = 1/60
Sangeeta 1 day work = 1/80
2 days Parth alone = 2 × 1/40 = 1/20
3rd day all three = 1/40 + 1/60 + 1/80 = 13/240 (LCM of 40, 60, 80 = 240)
Work in 3 days = 1/20 + 13/240 = 5/48
In 27 days (9 cycles) work = 9 × 5/48 = 15/16
Left work = 1/16
Day 28 & 29 → Parth = 2 × 1/40 = 1/20
Left = 1/16 − 1/20 = 1/80
Day 30 → all three = 13/240
Time = (1/80) ÷ (13/240) = 3/13 day
Total time = 29 + 3/13 = 29 days