A can finish a piece of work in 12 days, while B can do it in 15 days. If both work together, what time will they take to do the work?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{20}{3}\) days
Work done in one day adds up when people work together: A does \(\frac{1}{12}\) of the work in a day and B does \(\frac{1}{15}\).
Together in one day: \(\displaystyle\frac{1}{12}+\frac{1}{15}=\frac{5+4}{60}=\frac{3}{20}\) of the work
Time to finish the whole work \(\displaystyle=\frac{20}{3}\) days, that is, \(6\frac{2}{3}\) days
Shortcut:
For two workers, time together = product of their times ÷ sum of their times
\(\displaystyle\frac{12\times15}{12+15}=\frac{180}{27}=\frac{20}{3}\) days