As you've got numbers in the answer choices, I'd prefer using the answer choices and working backwards to arrive at the required answer. It's always good to start with the middle/third option.
Also, if you can see numbers that might be related in some way (multiples, divisors, etc), try to use them.
In the question stem, we've got the numbers 20 and 45 - both are multiples of 5. So, I'd personally use a multiple of 5 present in the answer choices to begin with. Here, 4 of the 5 choices are multiples of 5, making it a bit difficult to choose a number - so I'd go with option 3.
Let the days taken by Jose be 'A' days and that taken by Jane be 'B' days. We're told that Jane is more efficient than Jose which means that Jane will take fewer number of days to complete the work as compared to Jose. Therefore, A > B
Now, using option C i.e. 60 days to be the time taken by Jose to complete the work,
Working together, A and B take 20 days to complete the work.
Therefore, 1/A + 1/B = 1/20
Substituting A = 60 and solving for B, we get B = 30 days
We know that Jose works and completes half of the work. Since Jose takes 60 days to complete the work, he would take 30 days to complete half the work.
Similarly, since Jane takes 30 days to complete the work, she would take 15 days to complete half the work.
So, in total, Jose and Jane take 45 days to complete the work - which is what is given in the question stem.
Hence Option C
is the correct answer.
Hope this helps
MBA Candidate 2015 | Georgetown University
McDonough School of Business