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Hello!
How do you solve this question? I tried to do it and got an answer of 11 days. Then I tried it a different way and got an answer with a fraction in it (not half). Any suggestions? The correct answer is 10, but I can't get to it.

As far as I can tell, John and Jane work together for 5 days before Jane becomes "indisposed", and by then have completed 2/3 of the task. Then I get stuck. Am I right even this far? Help!

1 John can complete a given task in 20 days. Jane will take only 12 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 4 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?
6
10
8
7.5 days
3.5 days

The question states that Jane stopped working 4 days before the work got over.

The immediate response that any of us would have is that John and Jane working together will complete (1/20 + 1/12)th of the work in a day i.e., 8/60th or (1/7.5)th of the work in a day. Therefore, they will complete the work in 7.5 days.

Hence, if Jane stopped working 4 days before the work got over, she worked for 3.5 days.

However, there is a small catch to the above logic. The question does not state that Jane stopped working 4 days before the day when the work would have got over had they worked together to complete the entire project. The question states that Jane stopped working 4 days before the day the work got over.

We can solve this problem in two ways - the first is following the logic
If Jane stopped working 4 days before the work actually got over, then John alone worked for the last 4 days.

During these 4 days, John would have completed (4/20)th of the work or 1/5th of the work.

Hence, the remaining 4/5ths of the work was completed by John and Jane working together.

We know that John and Jane take 7.5 days to complete the entire task if they work together. Therefore, they will take 80% of that time to complete 4/5ths of the task. That is 6 days.

So, they worked together for 6 days and then John worked alone for 4 days. Hence, the work was done in 10 days.

The alternate method

Let 'y' be the number of days in whcih the work got over.

Then John worked all y days and Jane worked only 'y-4' days.
Hence, y/20 + (y-4)/12 = 1.

Solve this equation and you will get y = 10