A completes a work in 7 days. B completes the same work in 9 days. What will be the time taken in completing the same work if both A & B work together?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{63}{16}\) days
Work is added through one day’s work: a person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it each day, and working together their daily shares add up.
A’s one day’s work \(=\frac{1}{7}\); B’s \(=\frac{1}{9}\)
Together in one day: \(\displaystyle\frac{1}{7}+\frac{1}{9}=\frac{9+7}{63}=\frac{16}{63}\)
Time for the whole work \(\displaystyle =\frac{63}{16}\) days, about 3.9 days
Shortcut:
For two people taking \(a\) and \(b\) days, the time together is \(\displaystyle\frac{ab}{a+b}\)
\(\displaystyle\frac{7\times9}{7+9}=\frac{63}{16}\) days