Parth, Rizwan and Sangeeta can do a piece of work in 40, 60 and 80 days. Parth works daily, but Rizwan & Sangeeta assist him every 3rd day. In how many days will the work be done?

Correct option is D

Given:
Parth can do the work in 40 days
Rizwan can do the work in 60 days
Sangeeta can do the work in 80 days
Parth works daily
 Rizwan & Sangeeta assist him every 3rd day
Formula Used:
Work Rate = Total Work / Days
Work Done = Rate × Time
Solution:
Total Work = LCM(40, 60, 80) = 240 units
Efficiency of Parth = 240/40 = 6 units/day
Efficiency of Rizwan = 240/60 = 4 units/day
Efficiency of Sangeeta = 240/80 = 3 units/day
 Work in 3-day cycle:
Day 1: Parth = 6 units
Day 2: Parth = 6 units
Day 3: Parth + Rizwan + Sangeeta = 6 + 4 + 3 = 13 units
Total in 3 days = 25 units
Full cycles:
240 ÷ 25 = 9 full cycles (225 units) → 27 days
Remaining work = 15 units
Day 28: Parth = 6 units → remaining 9
Day 29: Parth = 6 units → remaining 3
Day 30: All work at 13 units/day → $$\frac 3{13}$$​ day needed
Final Time = 29 + $$\frac 3{13} = \frac{380}{13}$$​ days ≈ 29$$\frac 3{13}$$​ days