A can complete a piece of work in 10 days, B in 15 days and C in 20 days. A and C worked together for 2 days and then A was replaced by B. In how many days, altogether, was the work completed?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8 days
Each worker does a fixed share of the work every day, and workers who work together add their daily shares. The work done by A and C in the first 2 days is taken off, and B and C finish what is left.
Assuming the total work to be 60 units (the LCM of 10, 15 and 20):
A does \(60\div10=6\) units a day, B \(60\div15=4\) and C \(60\div20=3\)
A and C in 2 days: \(2\times(6+3)=18\) units
Work left: \(60-18=42\) units, done by B and C at \(4+3=7\) units a day
Time for it: \(42\div7=6\) days
Total time: \(2+6=8\) days