UGC NET Questions (Paper – 1)

To find the compound ratio p:s we multiply the fractional forms of the three given ratios: (3/5) × (10/11) × (4/7). The numerator becomes 3 × 10 × 4 = 120 and the denominator becomes 5 × 11 × 7 = 385. Simplifying 120/385 by dividing numerator and denominator by 5 gives 24/77. Therefore, the compound ratio p:s is 24:77.

Option A:
Option A, 12:35, could come from multiplying only part of the factors or simplifying incorrectly, for example by missing one of the denominators. If we back-calculate using 12:35, the intermediate ratios cannot be reconciled with 3:5, 10:11 and 4:7 simultaneously. Hence 12:35 does not reflect the full chained effect of all three ratios.

Option B:
Option B is correct because it directly results from the precise product (3/5) × (10/11) × (4/7) after proper simplification. Each given ratio is fully accounted for, and the cancellation is done using a common factor of 5, leading uniquely to 24:77. No other option preserves all three relationships in a single combined ratio.

Option C:
Option C, 24:49, keeps the correct numerator 24 but replaces 77 with 49, which is the denominator of only part of the product. This ignores the contribution of one of the original ratios when forming the compound. As a result, 24:49 cannot be the correct chain ratio from p to s.

Option D:
Option D, 30:77, uses the correct denominator but an inflated numerator, perhaps from erroneous multiplication 3 × 10 = 30 without considering the factor 4 and required simplification. When we test 30:77 against the given ratios, it fails to reproduce them, so 30:77 is not valid.

The compound ratio a:d is obtained by multiplying the fractional equivalents of the given ratios: (2/3) × (4/5) × (6/7). This product is (2 × 4 × 6)/(3 × 5 × 7) = 48/105. Simplifying 48/105 by dividing numerator and denominator by 3 gives 16/35. Hence, the compound ratio a:d is 16:35.

Option A:
Option A, 8:35, halves the correct numerator while keeping the denominator, so it does not correspond to the true product 48/105. If we tried to reconstruct the intermediate ratios from 8:35, they would not match 2:3, 4:5 and 6:7 simultaneously. Thus 8:35 is not consistent with the combined effect of the three ratios.

Option B:
Option B, 16:21, uses the correct numerator 16 but an incorrect denominator 21. The fraction 16/21 does not equal 48/105, because 16/21 would simplify to a different value. Therefore, it does not represent the compound ratio derived from the data.

Option C:
Option C, 8:21, is even further from the correct proportion, altering both numerator and denominator in ways not justified by the multiplication of the three given ratios. This option cannot be related back to the original conditions without violating at least one of the ratios.

Option D:
Option D is correct because 16:35 is exactly the simplified form of 48:105, the product of 2:3, 4:5 and 6:7. It correctly aggregates the effect of the three separate proportional relationships into one single ratio.

From a:b = 5:8 we can take a = 5k and b = 8k. From b:c = 12:7 we can take b = 12m and c = 7m. Equating b gives 8k = 12m, so m = 2k/3. Substituting back, c = 7m = 14k/3 and a = 5k, so a:c = 5k : 14k/3 = 15:14. Thus, the correct compound ratio of a to c is 15:14, obtained by consistently aligning the common middle term b.

Option A:
Option A, 5:7, might be guessed by combining the first numerator and second denominator, but it ignores the necessary scaling to make b consistent in both ratios. When we attempt to reconstruct the values from 5:7, the intermediate b does not match both given relationships simultaneously.

Option B:
Option B, 10:7, would emerge if we simply doubled the first ratio 5:8 in the numerator, but there is no justification for such doubling when combining with b:c = 12:7. Using 10:7 as a:c would not reproduce b as a common proportional term in both equations.

Option C:
Option C is correct because it follows from a systematic method: either multiply the fractions (5/8) × (12/7) and simplify, or explicitly equate b and solve for a and c. Both approaches lead to 15/14, which translates to the ratio 15:14. This ensures full consistency with both starting ratios.

Option D:
Option D, 15:16, uses the correct numerator 15 but pairs it with 16, which does not arise from any coherent simplification of the product of 5/8 and 12/7. If we assumed a:c = 15:16, the back-calculated intermediate values would conflict with the original ratio data.