Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1 / 3 as efficiently as he actually did the work, then they would have completed the work in 3 days. Find the time for A to complete the job alone?

Efficiency is proportional to work done per day. Work done per day N number of days
= Amount of work done. Considering efficience of A and B initially as 1.
Let A alone can do the work in M days and B alone can do the same work in N days.
Then, 5/M + 5/N = Total work done = 1
Since efficiency of A and B are 2 and 1/3 respectively
⇒ 6/M + 1/N = 1 ....(i)
and 1/M + 1/N = 5 .....(ii)
Now, subtracting equation (ii) from equation (i), we have M = 25/4 = 6¹/₄ days.