UGC NET Questions (Paper – 1)

Let the total work be 1 unit. A’s work rate is 1/20 per day, and A and B together work at 1/12 per day. B’s rate is the difference, 1/12 − 1/20. Taking the least common multiple of 12 and 20 as 60, we get B’s rate as (5 − 3)/60 = 2/60 = 1/30 per day. Thus, B alone would need 30 days to complete the work.

Option A:
Option A, 24 days, corresponds to a rate of 1/24, which when added to A’s rate of 1/20 would give a combined rate different from 1/12. It does not match the given completion time when working together.

Option B:
Option B, 30 days, matches a work rate of 1/30. Adding this to A’s rate 1/20 yields 1/12, which is consistent with the statement that they finish the work together in 12 days.

Option C:
Option C, 36 days, gives a rate of 1/36, and 1/20 + 1/36 does not add up to 1/12, so it contradicts the given joint time.

Option D:
Option D, 60 days, implies too slow a rate for B, and combined with A it would result in a joint time longer than 12 days.