A and B can do a work in 10 days and 20 days respectively. They started the work together but A left the work 2 days before the completion of the work. In how many days was the work completed?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 8
Take the whole work as 20 units, the LCM of 10 and 20. B works on all the days, but A stops 2 days before the end, so A works 2 days fewer than B.
A does \(20\div10=2\) units a day; B does \(20\div20=1\) unit a day
Let the work take \(t\) days: A works \(t-2\) days and B works \(t\) days
\(2(t-2)+1\times t=20\)
\(3t-4=20\), so \(3t=24\) and \(t=8\) days