Jayati and Archana can do a piece of work in 10 days and Jayati can do the same work in 12 days. In how many days can Archana do the same work alone?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 60 days
A person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it in one day, and the one-day work of people working together is added. Archana’s one-day work is therefore the joint one-day work minus Jayati’s.
Jayati and Archana together: \(\frac{1}{10}\) of the work a day
Jayati alone: \(\frac{1}{12}\) of the work a day
Archana alone: \(\displaystyle\frac{1}{10}-\frac{1}{12}=\frac{6-5}{60}=\frac{1}{60}\) of the work a day, so she needs 60 days
Shortcut: Take the whole work as 60 units, the LCM of 10 and 12.
Together: \(60\div10=6\) units a day
Jayati: \(60\div12=5\) units a day
Archana: \(6-5=1\) unit a day, so 60 days