P completed \(\frac{2}{5}\) part of certain work in 12 days. Further, Q completed the rest of the work in 18 days. In how many days could P and Q complete the work, if they worked together?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 15
In time-and-work questions, a person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it in one day, and when two people work together their one-day work is added. So the time each takes alone is found first.
P does \(\frac{2}{5}\) of the work in 12 days, so the whole work in \(\displaystyle 12\times\frac{5}{2}=30\) days
Q does the rest, \(\displaystyle 1-\frac{2}{5}=\frac{3}{5}\), in 18 days, so the whole work in \(\displaystyle 18\times\frac{5}{3}=30\) days
One-day work together: \(\displaystyle \frac{1}{30}+\frac{1}{30}=\frac{1}{15}\)
Together they finish the work in 15 days