A can do a piece of work alone in 15 days, while B completes the same piece of work alone in 12 days. If they work on it together for 5 days, then the fraction of the work that will be left is:
Show answer & explanation
Correct answer: C
Explanation
the correct answer is option 3 i.e 1/4.
We can start by first finding the fraction of the work that A can do in one day and the fraction of the work that B can do in one day.
A can do the whole work in 15 days, so in one day, A can do 1/15th of the work. Similarly, B can do the whole work in 12 days, so in one day, B can do 1/12th of the work.
If they work together for 5 days, then in 5 days, the fraction of the work that they can do together is:
5[(1/15) + (1/12)] = 5[(4/60) + (5/60)] = 5(9/60) = 3/4
So they would have completed 3/4 of the work in 5 days. Therefore, the fraction of the work that will be left is:
1 - 3/4 = 1/4
So after 5 days of working together, there will be 1/4 of the work left to be done.