UGC NET Questions (Paper – 1)

The ratio 3:2 means that out of every 5 students, 3 are boys and 2 are girls. Since the total number of students is 30, we first find how many groups of 5 there are: 30 ÷ 5 = 6. The number of boys is then 3 × 6 = 18. Hence, there are 18 boys in the class.

Option A:
If there were 12 boys, then the ratio of boys to girls would not be 3:2 with a total of 30 students. Specifically, 12 boys would leave 18 girls, giving a ratio of 12:18, which simplifies to 2:3, not 3:2. Therefore, this option does not satisfy the given ratio.

Option B:
If there were 15 boys, the remaining 15 students would be girls, resulting in a ratio of 15:15 or 1:1. This is very different from the required ratio of 3:2. Thus, option B is not correct.

Option C:
18 is correct because it maintains the ratio 3:2 with a total of 30 students. With 18 boys and 12 girls, the ratio 18:12 simplifies to 3:2 as required. This method demonstrates how ratio and total together determine individual quantities in aptitude problems.

Option D:
If there were 20 boys, only 10 girls would remain, giving a ratio of 20:10 or 2:1, which does not match 3:2. This inconsistency shows that 20 is not the correct number of boys.

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.

If a person completes the entire work in 8 days working at a constant rate, then each day they complete 1/8 of the total work. This follows from the idea that total work is taken as 1 and is divided equally among the number of days. The daily work rate is thus the reciprocal of the total time. Therefore, 1/8 is the correct fraction of work done in one day.

Option A:
1/6 would imply that the work is fully completed in 6 days, because 6 times 1/6 equals 1. However, the question clearly states that the work is completed in 8 days. Hence, 1/6 overestimates the daily work rate and is inconsistent with the given information.

Option B:
1/4 would mean completing the work in 4 days, since four days of work at this rate would make a full unit of work. This contradicts the stated time of 8 days. Therefore, 1/4 is not compatible with the conditions of the problem.

Option C:
The fraction 1/8 is correct because multiplying it by the total number of days, 8, yields 1, representing the entire work: 8 × 1/8 = 1. This reflects the standard unitary method used in time and work questions. Recognising that the daily rate is the reciprocal of total time simplifies many such problems on competitive exams.

Option D:
2/8 simplifies to 1/4, which, as explained earlier, corresponds to finishing the work in 4 days rather than 8. Using this fraction would contradict the given total time to completion. As a result, 2/8 is not the correct fraction of work done in one day in this scenario.