UGC NET Questions (Paper – 1)

Statements A, B and C state the standard time–work model: one-day work as 1/n, combined rates added and inverse relation between time and rate. Statement E is also true since many problems can be set up and solved using simple linear equations in the unknown rates. Statement D is false because if A is twice as fast as B, A will take half the time, not twice. Therefore, the combination A, B, C and E only is correct.

Option A:
Option A is incomplete because it leaves out E and thus fails to mention the useful algebraic viewpoint that rates can be handled by linear equations. Without E, the picture of modelling is not fully captured.

Option B:
Option B is correct since it collects all the true statements and excludes D, which reverses the relationship between speed and time. It reflects exactly how NET aspirants are expected to reason about time and work problems.

Option C:
Option C is incorrect because it includes D, the wrong claim about time for a faster worker, even though it also lists some true statements. Including a false statement invalidates the combination.

Option D:
Option D is also wrong as it retains D and omits A, failing to state the fundamental definition of one-day work while endorsing an incorrect comparison of times.

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.

A’s one-day work is 1/15 of the job and B’s one-day work is 1/20 of the job. Their combined daily work is 1/15 + 1/20. The least common multiple of 15 and 20 is 60, so this becomes 4/60 + 3/60 = 7/60 of the work per day. The total time to complete one whole work is therefore 1 ÷ (7/60) = 60/7 ≈ 8.57 days. Among the integer options given, 9 days is the closest approximation to 60/7, so it is the most appropriate answer.

Option A:
Option A, 8 days, underestimates the exact value of about 8.57 days; in 8 days they would complete only 8 × 7/60 = 56/60 of the work, leaving some part unfinished.

Option B:
Option B, 9 days, is the nearest whole number to 60/7 and slightly overestimates the exact time, which is why it is the best choice among the given options.

Option C:
Option C, 10 days, deviates further from the exact value and would correspond to a slower combined rate than actually calculated.

Option D:
Option D, 12 days, is much larger than 60/7 and ignores the productivity gain from having both A and B work together.