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.

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.

If A fills the tank in 12 hours, A’s one-hour work is 1/12; for B it is 1/18, and for C it is 1/36. The ratio A:B:C in one hour is (1/12):(1/18):(1/36). Taking the LCM of 12, 18 and 36 as 36, we get 3:2:1 as the simplified ratio. Thus, A, B and C complete the work in the ratio 3:2:1 per hour.

Option A:
Option A, 6:4:3, represents 6:4:3 which, when normalised, does not match 1/12:1/18:1/36. Dividing these by 3 gives 2:4/3:1, which is not proportional to 3:2:1, so it misstates the relative speeds of the taps.

Option B:
Option B, 3:2:2, suggests that B and C work at the same rate, which contradicts the given times. Since C takes 36 hours, which is double B’s 18 hours, C must work at half of B’s rate, not the same rate. Therefore, 3:2:2 is inconsistent with the time data.

Option C:
Option C, 2:3:6, would imply that C is working fastest, with the largest share of work per hour, while in reality C is the slowest tap. This directly contradicts the inverse relationship between time and rate, so 2:3:6 cannot be correct.

Option D:
Option D is correct because converting the one-hour work fractions to a common denominator and simplifying gives 3:2:1. This ratio accurately reflects that A is fastest, B is intermediate and C is slowest, in exact accordance with their filling times.