Joint Work Time Fractional Days – UGC NET Question

A’s one-day work is 1/12 of the job and B’s one-day work is 1/20 of the job. The combined one-day work is therefore 1/12 + 1/20. Using the least common multiple of 12 and 20, which is 60, this becomes (5 + 3) / 60 = 8 / 60 = 2 / 15. The total time required is the reciprocal of 2 / 15, which is 15 / 2 or 7.5 days. Thus, together they will finish the work in 7.5 days.

Option A:
Option A, 6 days, is too small and would imply a higher combined rate than 2/15 per day. It suggests that the two workers together are even more efficient than the calculations show.

Option B:
Option B accurately reflects the reciprocal of the combined daily work fraction. It respects the principle that joint work rates add and that the total time is found by inverting the sum.

Option C:
Option C, 8 days, overestimates the time and corresponds to a smaller combined rate than the actual 2/15 of the work per day.

Option D:
Option D, 10 days, is even less efficient and ignores the substantial contribution B adds when working alongside A.