A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 15 days
In work questions the work done in one day is added: if a person finishes the work in \(n\) days, he does \(\frac{1}{n}\) of it each day. B’s share comes from the difference of the two rates given, and working half a day halves it.
A and B together: \(\frac{1}{12}\) of the work a day; A alone: \(\frac{1}{20}\)
B alone: \(\displaystyle\frac{1}{12}-\frac{1}{20}=\frac{5-3}{60}=\frac{1}{30}\) a day
B for half a day: \(\displaystyle\frac{1}{2}\times\frac{1}{30}=\frac{1}{60}\) a day
A full day and B half a day: \(\displaystyle\frac{1}{20}+\frac{1}{60}=\frac{4}{60}=\frac{1}{15}\) a day, so the work takes 15 days