UGC NET Questions (Paper – 1)

If A alone finishes the work in 10 days, A’s one-day work is 1/10 of the job. If B alone finishes in 15 days, B’s one-day work is 1/15. The ratio of work done by A to work done by B in one day is (1/10):(1/15) = 15:10, which simplifies to 3:2. Thus, the required ratio is 3:2.

Option A:
Option A, 2:3, reverses the correct comparison and implies B does more work per day than A, suggesting B is faster. This contradicts the completion times, because A finishes in fewer days than B and must therefore have the higher daily rate.

Option B:
Option B, 4:3, does not match the exact fraction (1/10)/(1/15) = 15/10 = 3/2. While 4:3 is close numerically to 3:2, the calculation from the given times unambiguously leads to 3:2, not 4:3. Hence 4:3 is incorrect.

Option C:
Option C is correct because it faithfully reflects the inverse relationship between time and rate for a fixed amount of work. Shorter time (10 days) corresponds to a larger rate, and the ratio of these rates simplifies precisely to 3:2.

Option D:
Option D, 5:3, exaggerates the difference between the two rates beyond what is implied by 10 and 15 days. Using 5:3 would not produce the correct individual times if we converted back from the rate ratio, so it cannot be accepted.

Statements A, B and C are correct because they follow the standard work-rate model: daily work is reciprocal of time, combined rate is additive and rate and time are inversely related when total work is fixed. Statement E is also true, as time and work problems are common in competitive exams including UGC NET. Statement D is false, since doubling the number of workers at the same rate would halve the time, not double it. Hence, the combination that includes A, B, C and E and excludes D is correct.

Option A:
Option A is incomplete because although it lists three true statements, it omits E and therefore fails to acknowledge the practical relevance of time and work problems in exam contexts. Without E, the question’s aptitude orientation is underplayed.

Option B:
Option B is correct as it gathers all four true statements about how work rate is modelled and assessed in exams, and it rightly rejects D, which reverses the effect of doubling the workforce. This option matches the conceptual structure used in NET work-rate questions.

Option C:
Option C is wrong because it includes D, the incorrect statement about time doubling, and excludes A, missing the basic definition of one-day work. The presence of D makes the overall set invalid.

Option D:
Option D is incorrect since it excludes B and thus does not stress that combined work is the sum of individual works, while still omitting the false D. Even though A, C and E are true, leaving B out makes the description incomplete.

If A finishes the work in 12 days, A’s one-day work is 1/12. If B finishes in 18 days, B’s one-day work is 1/18. The ratio of A’s work to B’s work in one day is (1/12):(1/18) = 18:12, which simplifies to 3:2. Hence, the required ratio is 3:2.

Option A:
Option A, 2:3, is the inverse of the correct ratio. It would imply that B does more work per day than A, suggesting that B is faster, which contradicts the given completion times where A finishes in fewer days.

Option B:
Option B, 4:3, does not result from the fraction 1/12 divided by 1/18. If we equate 4:3 to 18:12, we see that 18:12 simplifies to 3:2, not 4:3. Thus 4:3 cannot represent the actual comparison of their daily work.

Option C:
Option C, 5:4, appears as a plausible ratio but has no basis in the calculations from 12 and 18 days. When we compute the exact fractions, 1/12 and 1/18, they do not simplify in a way that yields 5:4. Therefore, 5:4 is inconsistent with the numerical data.

Option D:
Option D is correct because it reflects the fact that A’s daily work is greater than B’s in the precise proportion 3:2. This means that for every 3 units of work A does in a day, B does 2 units, matching the relative speeds implied by their completion times.

Statements A and B correctly define speed and describe the inverse relationship between speed and time for a fixed distance. Statement E is also true because many aptitude questions demand consistent units, requiring conversions like km/h to m/s. Statement C is false since the average speed for a round trip with different speeds is given by the harmonic mean, not the simple arithmetic mean, and D is false because using consistent units, not different ones, avoids confusion. Therefore, the combination A, B and E only is correct.

Option A:
Option A is incomplete because although it includes two true statements, it omits E and thus fails to highlight the practical necessity of unit conversion in exam problems. Without E, the description of typical question features is not complete.

Option B:
Option B is correct as it collects all the true statements and rejects C and D, which misdescribe average speed and unit usage. It perfectly matches the conceptual treatment of time–speed–distance in UGC NET.

Option C:
Option C is wrong because it brings in C, which wrongly uses the arithmetic mean for round trips, and therefore mixes a false statement with true ones. This mathematical error invalidates the option.

Option D:
Option D is incorrect since it includes D, the mistaken claim about using different units, and omits A, which gives the core definition of speed. This combination misleads about both concept and practice.