UGC NET Questions (Paper – 1)

The work rate of A is 1/12 and that of B is 1/18 of the work per day. Together, their combined rate is 1/12 + 1/18 = (3 + 2)/36 = 5/36 of the work per day. The total time to complete one whole work at this rate is the reciprocal, which is 36/5 days, equal to 7.2 days. Hence, they can complete the work together in 7.2 days.

Option A:
If we assume 6 days, the combined work done would be 6 × (5/36) = 30/36 = 5/6 of the work, which is less than 1. This means the work would remain incomplete after 6 days, so 6 days is too little time and thus incorrect.

Option B:
If we choose 7 days, the total work done would be 7 × (5/36) = 35/36, still short of the full work. This value underestimates the time required, so 7 days is not an accurate answer for the exact completion.

Option C:
Assuming 8 days, the work done would be 8 × (5/36) = 40/36, which exceeds 1, meaning more than the total work is accounted for. This overestimates the time, indicating that 8 days is too long.

Option D:
7.2 days is correct because 36/5 is precisely the reciprocal of the combined rate 5/36. Writing it as 7.2 makes the decimal representation easier to interpret in numeric aptitude problems. This value ensures that the computed work equals exactly 1, satisfying the problem conditions.

Statements A and B give the usual representation of individual and combined work rates in time and work problems. Statement D is also correct because increasing the number of equally efficient workers generally reduces the time for a fixed job when total work is unchanged. Statement C is false, since a faster worker takes less time, and E is false because alternate-day work patterns depend on how many days are counted and cannot always be reduced to a simple average. Hence the correct set of statements is A, B and D only, matching option B.

Option A:
Option A is incomplete as it leaves out D, thereby ignoring the inverse relation between number of workers and time, which is a standard pattern tested in exam questions.

Option B:
Option B is correct because it collects the ideas of one-day work, combined rate and inverse proportionality while excluding C and E, which misstate how speed affects time and oversimplify alternate working-day scenarios.

Option C:
Option C is wrong since it brings in E, which incorrectly claims a simple average works in all alternate-day situations, and it omits B, so it both adds an error and loses a fundamental rule.

Option D:
Option D is incorrect because it includes C, which reverses the comparison of fast and slow workers, and it omits A, dropping the basic 1/x representation of one-day work.