Neha can complete a work in 6 days and Ishrat can complete the same work in 4 days. What will be the time taken by them to complete the same work together?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(2\displaystyle\frac{2}{5}\) days
When two people work together, their works for one day add up. The time they take together is the whole work divided by the part they finish together in one day.
Neha finishes \(\frac{1}{6}\) of the work in a day, Ishrat \(\frac{1}{4}\)
Together in one day: \(\displaystyle\frac{1}{6}+\frac{1}{4}=\frac{2+3}{12}=\frac{5}{12}\) of the work
Time taken together: \(\displaystyle\frac{12}{5}=2\frac{2}{5}\) days
Shortcut:
For two people taking \(a\) and \(b\) days, the time together is \(\displaystyle\frac{ab}{a+b}\)
\(\displaystyle\frac{6\times4}{6+4}=\frac{24}{10}=2.4\) days \(=2\frac{2}{5}\) days