Question : A, B, and C working separately can do a piece of work in 11 days, 20 days, and 55 days respectively. In how many days, the work will be completed if A is assisted by B and C on alternate days?
Option 1: 2 days
Option 2: 6 days
Option 3: 4 days
Option 4: 8 days
Correct Answer: 8 days
Solution : Given: A, B, and C can do a piece of work in 11 days, 20 days, and 55 days respectively. Total work = LCM of (11, 20, 55) = 220 units Efficiency of A =$\frac{220}{11}$ = 20 units Efficiency of B =$\frac{220}{20}$ = 11 units Efficiency of C =$\frac{220}{55}$ = 4 units 1st day of work (A and B) = (20 + 11) = 31 units 2nd day of work (A and C) = (20 + 4) = 24 units Total work done after 2 days = (31 + 24) = 55 units Total time taken =$\frac{220}{55}$ = 4 × 2 = 8 days Hence, the correct answer is 8 days.
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