Compound ratio across three ratios – UGC NET Question

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.