This question took me 2mins 2 secs which I feel is on the higher side. I need to work further on reducing the time taken because I knew the approach but just kind of missed a trick at the last point of the solution.
I followed a similar approach as per the work formula. My solution goes as follows --:
Jack : 8 hours to complete the job. Hence in 4 hours he will complete 1/2 of the job.
At this point Tom (who takes 12 hours for the job) joins in.
Together, Jack and Tom complete (1/8+1/12) of the job is 1 hour i.e. 5/24 of the job in 1 hour.
Here, I missed a simple trick i.e. 5/24 in 1 hour hence 24/5 for the entire job i.e. (24/5)/2 for half the job. This could have reduced my time about 10-15 secs.
I spent relatively longer time on this step. Since we need time for 1/2 of the job i.e. 12/24 it can be split as 5/24+5/24+2/24 i.e. 1 hour + 1 Hour + <~half hour.
Hence total time needed by Jack = 4 hours + ~2.5 Hours = greater than 6 hours but less than 6.5 hours. D is the only option hence I chose D.
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