UGC NET Questions (Paper – 1)

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.

A’s one day work is 1/10 of the job and B’s one day work is 1/15 of the job. When they work together, the daily work done is the sum of their individual rates: 1/10 + 1/15. Taking the LCM of 10 and 15 gives 30, so the combined rate is (3/30 + 2/30) = 5/30 = 1/6. Thus, together they complete 1/6 of the work each day and need 6 days to finish the entire work.

Option A:
Option A, 4 days, would imply a combined rate of 1/4 per day, which is higher than what A and B can achieve together. The actual sum of their rates does not support completion in 4 days.

Option B:
Option B, 5 days, would mean they do 1/5 of the work per day, requiring a combined rate larger than 1/6. However, the calculated total rate from their individual capacities is only 1/6.

Option C:
Option C is consistent with the reciprocal method: adding 1/10 and 1/15 gives 1/6, whose reciprocal is 6 days. This uses the standard approach for time and work problems and fits the given data exactly.

Option D:
Option D, 8 days, underestimates their combined productivity and corresponds to a rate of 1/8 per day, which is lower than the actual 1/6 per day.