UGC NET Questions (Paper – 1)

To find the compound ratio a:d, we multiply the fractional forms of each given ratio: (3/4) × (5/6) × (2/3). This product equals 30/72, which simplifies to 5/12 on reducing by the common factor 6. So the overall ratio of a to d is 5:12. Hence 5:12 is the only option that correctly represents the compound ratio of a to d.

Option A:
Option A is correct because it follows directly from the multiplication of the three given ratios and proper simplification of the resulting fraction. When we reduce 30/72, we divide numerator and denominator by 6 to obtain 5/12. This simplified form represents the true relationship between a and d after chaining all three ratios.

Option B:
Option B, 5:18, would correspond to a fraction 5/18 which is smaller than 5/12 and does not emerge from multiplying 3/4, 5/6 and 2/3. If we tried to reconstruct the intermediate ratios from 5:18, they would not match any of the given values. Therefore, 5:18 cannot be the correct compound ratio.

Option C:
Option C, 10:27, appears similar in form but is not equivalent to 5:12 when written as a fraction. 10/27 is approximately 0.37, whereas 5/12 is approximately 0.4167, so they are clearly different values. It does not result from multiplying the given three ratios in sequence.

Option D:
Option D, 5:9, would give a fraction 5/9 which is larger than 5/12 and does not match the product 30/72 after simplification. If 5:9 were correct, reversing the calculation would not recover the original ratios 3:4, 5:6 and 2:3. Hence, 5:9 is an incorrect representation of a:d.

Let the unknown number be N. If 25% of N is 60, then 0.25N = 60. Solving this equation gives N = 60 ÷ 0.25 = 240. To find 40% of this number, we compute 0.40 × 240, which equals 96. Thus, 40% of the number is 96.

Option A:
Option A, 80, corresponds to one third of 240, not 40%, and would arise from mixing up the percentage multipliers. It does not follow from the given condition.

Option B:
Option B, 90, is 37.5% of 240 and again has no direct link to the required 40% rate. It reflects an incorrect multiplication step.

Option C:
Option C is obtained by first recovering the full value of the number from the 25% information and then correctly applying the 40% factor to it. The arithmetic is consistent at each stage and produces 96.

Option D:
Option D, 100, is slightly higher than the correct value and might come from rounding or a mistaken assumption that 40% is close to half, but it is not the exact result.

Let the total work be 1 unit. A’s work rate is 1/20 per day, and A and B together work at 1/12 per day. B’s rate is the difference, 1/12 − 1/20. Taking the least common multiple of 12 and 20 as 60, we get B’s rate as (5 − 3)/60 = 2/60 = 1/30 per day. Thus, B alone would need 30 days to complete the work.

Option A:
Option A, 24 days, corresponds to a rate of 1/24, which when added to A’s rate of 1/20 would give a combined rate different from 1/12. It does not match the given completion time when working together.

Option B:
Option B, 30 days, matches a work rate of 1/30. Adding this to A’s rate 1/20 yields 1/12, which is consistent with the statement that they finish the work together in 12 days.

Option C:
Option C, 36 days, gives a rate of 1/36, and 1/20 + 1/36 does not add up to 1/12, so it contradicts the given joint time.

Option D:
Option D, 60 days, implies too slow a rate for B, and combined with A it would result in a joint time longer than 12 days.