A, B and C can do a piece of work in 20 days, 25 days and 30 days respectively. They work one at a time, one day each in turn: A on the first day, B on the second day, C on the third day, A again on the fourth day, and so on. In how many days will the work be finished?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(24\frac{4}{15}\)
Take the work as the LCM of 20, 25 and 30, that is 300 units. Count full 3-day rounds first, then see who finishes the little that is left.
Daily work: A \(=\frac{300}{20}=15\) units, B \(=\frac{300}{25}=12\) units, C \(=\frac{300}{30}=10\) units
One round of 3 days (A, B, C) \(=15+12+10=37\) units
8 rounds \(=8\times37=296\) units in \(8\times3=24\) days
Work left \(=300-296=4\) units, done by A on day 25
A needs \(\frac{4}{15}\) of a day for 4 units
Total time \(\displaystyle =24\frac{4}{15}\) days