A, B and C can do a piece of work in 9, 12 and 18 days respectively. All three start the work together. After 2 days A leaves, and after 3 more days B also leaves. In how many days from the start will the whole work be finished?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(6\frac{1}{2}\)
Take the work as the LCM of 9, 12 and 18, that is 36 units, and add the work of each stretch until it reaches 36.
Daily work: A \(=4\) units, B \(=3\) units, C \(=2\) units
First 2 days, all three: \(2\times(4+3+2)=18\) units
Next 3 days, B and C: \(3\times(3+2)=15\) units; total 33 units
C alone does the remaining \(36-33=3\) units in \(\frac{3}{2}=1\frac{1}{2}\) days
Total time \(=2+3+1\frac{1}{2}=6\frac{1}{2}\) days
The work is finished in \(6\frac{1}{2}\) days.