Combined Work of Two Persons – UGC NET Question

A’s one day work is 1/12 of the job and B’s one day work is 1/18 of the job. When they work together, their combined daily work is 1/12 + 1/18. The least common multiple of 12 and 18 is 36, so their combined rate becomes 3/36 + 2/36 = 5/36 of the work per day. The total time to complete one whole work is therefore 1 ÷ (5/36) = 36/5 = 7.2 days.

Option A:
Option A, 7 days, would require a combined rate of 1/7 per day, which is larger than the actual 5/36 and therefore inconsistent with the calculated work rates. It underestimates the time needed.

Option B:
Option B, 7.2 days, corresponds exactly to 36/5 days, which arises from adding the reciprocals of 12 and 18 correctly. This option respects the standard reciprocal method and therefore matches the true combined time.

Option C:
Option C, 8 days, implies a daily work rate of 1/8, which is smaller than 5/36. It overestimates the time required and is not supported by the given individual efficiencies.

Option D:
Option D, 9 days, further slows the work rate to 1/9 per day and contradicts the fact that together A and B can accomplish more work per day than either alone.