A, B and C can do a piece of work in 15 days, 30 days and 40 days, respectively. A starts working on the first day, A and B works on the second day and A and C works on the third day. This pattern is repeated till the work gets completed. In how many days will the work be over?

Correct option is A

Given:

A can complete the work in 15 days 

B can complete the work in 30 days  

C can complete the work in 40 days

Work pattern:

Day 1 → A

Day 2 → A + B

Day 3 → A + C

Repeat...

Formula Used:

Total work = Number of days × Daily work

Solution: 

Total work = LCM(15, 30, 40) = 120 units 

A's rate = 8 units/day

B's rate = 4 units/day

C's rate = 3 units/day

Cycle-wise breakdown:

Day 1: A → 8 units

Day 2: A + B → 8 + 4 = 12 units

Day 3: A + C → 8 + 3 = 11 units

Total per 3-day cycle = 8 + 12 + 11 = 31 units

After 3 complete cycles (9 days):

Total work done = 3 × 31 = 93 units

Remaining work = 120 - 93 = 27 units

Continuing pattern:

Day 10: A → 8 units → remaining = 19 units

Day 11: A + B → 12 units → remaining = 7 units

On Day 12: A + C work for 7 unit 

So time take  = $$\frac{7}{11}$$​​

Total time taken = 9 + 1 + 1 + $$\frac{7}{11}$$ = 11$$\frac{7}{11}$$​  days