UGC NET Questions (Paper – 1)

The rate of work of one man can be found by noting that 4 men finish the work in 12 days, so 1 man’s daily work is 1 divided by (4 × 12), which is 1/48. Similarly, 6 women finish the work in 18 days, so 1 woman’s daily work is 1 divided by (6 × 18), which is 1/108. For 2 men and 3 women together, the combined daily work is 2/48 plus 3/108. Simplifying, 2/48 is 1/24 and 3/108 is 1/36. The sum of 1/24 and 1/36 is 5/72. The total time to complete one work is 1 divided by 5/72, which equals 72/5 or 14.4 days.

Option A:
Option A, 12 days, would require the mixed group to be as effective as 4 men alone, which is not supported by the calculated rate of 5/72 per day. The combination of 2 men and 3 women is somewhat less efficient than that.

Option B:
Option B uses individual rates to compute a combined rate and then takes the reciprocal to determine total time. This standard time and work approach produces 14.4 days, which is the only option consistent with the carefully derived daily work rate.

Option C:
Option C, 15 days, is close to but not equal to 14.4 days, indicating a rounded or estimated value that does not precisely follow the computed reciprocal.

Option D:
Option D, 18 days, equates to the time taken by 6 women alone and ignores the additional contribution from the 2 men working alongside them.

Pipe A fills 1/10 of the tank per hour, pipe B fills 1/15 per hour, and pipe C empties 1/30 per hour. The net hourly work rate when all three are open is 1/10 + 1/15 − 1/30. Using 30 as the common denominator, this becomes 3/30 + 2/30 − 1/30 = 4/30 = 2/15 of the tank per hour. The time to fill the tank is therefore 1 ÷ (2/15) = 15/2 = 7.5 hours, which matches Option B.

Option A:
Option A, 5 hours, would require a net rate of 1/5 per hour, which is much faster than the computed 2/15 and not achievable with the given pipes.

Option B:
Option B, 7.5 hours, is exactly the reciprocal of the net rate 2/15 and correctly represents the time taken to fill the tank with all three pipes open.

Option C:
Option C, 8 hours, corresponds to a net rate of 1/8 per hour, slower than 2/15, and inconsistent with the detailed rate computation.

Option D:
Option D, 10 hours, duplicates the time taken by pipe A alone and ignores the additional inflow from B and the outflow from C, so it cannot be correct.

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.

A’s one day work is 1/12 of the job and B’s one day work is 1/18 of the job. When they work together, their combined daily work is 1/12 + 1/18. The least common multiple of 12 and 18 is 36, so their combined rate becomes 3/36 + 2/36 = 5/36 of the work per day. The total time to complete one whole work is therefore 1 ÷ (5/36) = 36/5 = 7.2 days.

Option A:
Option A, 7 days, would require a combined rate of 1/7 per day, which is larger than the actual 5/36 and therefore inconsistent with the calculated work rates. It underestimates the time needed.

Option B:
Option B, 7.2 days, corresponds exactly to 36/5 days, which arises from adding the reciprocals of 12 and 18 correctly. This option respects the standard reciprocal method and therefore matches the true combined time.

Option C:
Option C, 8 days, implies a daily work rate of 1/8, which is smaller than 5/36. It overestimates the time required and is not supported by the given individual efficiencies.

Option D:
Option D, 9 days, further slows the work rate to 1/9 per day and contradicts the fact that together A and B can accomplish more work per day than either alone.

A’s one day work is 1/10 of the job and B’s one day work is 1/15 of the job. When they work together, the daily work done is the sum of their individual rates: 1/10 + 1/15. Taking the LCM of 10 and 15 gives 30, so the combined rate is (3/30 + 2/30) = 5/30 = 1/6. Thus, together they complete 1/6 of the work each day and need 6 days to finish the entire work.

Option A:
Option A, 4 days, would imply a combined rate of 1/4 per day, which is higher than what A and B can achieve together. The actual sum of their rates does not support completion in 4 days.

Option B:
Option B, 5 days, would mean they do 1/5 of the work per day, requiring a combined rate larger than 1/6. However, the calculated total rate from their individual capacities is only 1/6.

Option C:
Option C is consistent with the reciprocal method: adding 1/10 and 1/15 gives 1/6, whose reciprocal is 6 days. This uses the standard approach for time and work problems and fits the given data exactly.

Option D:
Option D, 8 days, underestimates their combined productivity and corresponds to a rate of 1/8 per day, which is lower than the actual 1/6 per day.

The daily work rates of A, B and C are 1/10, 1/15 and 1/30 respectively. Working together, their combined rate is 1/10 + 1/15 + 1/30, which simplifies to 1/5 of the work per day. In the first 2 days, they therefore complete 2 × 1/5 = 2/5 of the work. The remaining 3/5 of the work is then done by B and C alone, whose combined rate is 1/15 + 1/30 = 1/10. At this rate, they need (3/5) ÷ (1/10) = 6 more days. Adding the initial 2 days gives a total of 8 days to finish the work.

Option A:
Option A correctly adds the contributions in the two phases: an initial phase with three workers and a second phase with two workers. It respects the different group rates and sums the corresponding time intervals to reach 8 days.

Option B:
Option B, 7 days, underestimates the time and would require the second phase to progress faster than the combined rate of B and C allows.

Option C:
Option C, 6 days, is only the time needed for B and C to complete 3/5 of the work, not including the first 2 days already spent by all three.

Option D:
Option D, 9 days, overestimates the total time and suggests a slower rate than actually achieved by the workers as a group.