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?

Correct option is B

Given:

P: 25 days , Q: 30 days

R: 36 days,  S: 40 days 

4-day cycle: Q, S, P, R

Formula Used: 

Total work = Rate × Time

​Solution:​

Total work = LCM(25, 30, 36, 40) = 1800 units

Daily efficiencies:

Q = $$\frac{1800}{30}$$ = 60 units/day

S = $$\frac{1800}{40}$$ = 45 units/day

P = $$\frac{1800}{25}$$ = 72 units/day

R = $$\frac{1800}{36}$$ = 50 units/day

One 4-day cycle work = 60 + 45 + 72 + 50 = 227 units

Number of cycles to complete total work = $$\frac{1800}{227} \approx$$​ 7.93 cycles

Thus, 7 full cycles (28 days) complete 1589 units of work.

Remaining work = 1800 - 1589 = 211 units

Day 29,Q works = 60 unit  → Remaining work = 211 - 60 = 151 units

Day 30,  S works = 45 units → Remaining work = 151 - 45 = 106 units

Day 31, P works = 72 units → Remaining work = 106 - 72 = 34 units

Now,  time taken by R to complete 34 unit work,

$$\frac{34}{50}$$​ = $$\frac{17}{25}$$​ days

Thus, the total time taken = 28 + 3 + $$\frac{17}{25}$$​ = 31$$\frac{17}{25}$$​ days