Ratio of sums from linked ratios – UGC NET Question

From a:b = 7:9, we can take a = 7k and b = 9k. From b:c = 3:4, take b = 3m and c = 4m. Equating b gives 9k = 3m, so m = 3k and c = 4m = 12k. Now a + b = 7k + 9k = 16k and b + c = 9k + 12k = 21k. Therefore, (a + b):(b + c) = 16:21.

Option A:
Option A, 7:9, simply restates the original a:b ratio and does not consider the contributions from c in b + c. Because the question asks for the ratio of sums, not of individual terms, 7:9 fails to capture the required combined relationships.

Option B:
Option B is correct because it arises from expressing a, b and c in terms of a single parameter k that satisfies both given ratios. Only after this alignment can we reliably compute a + b and b + c. The final ratio 16:21 cannot be obtained by any shortcut that ignores this common scaling step.

Option C:
Option C, 4:7, might be guessed by incorrectly mixing the numerators of the given ratios, but it is not supported by the actual expressions for a + b and b + c. Substituting 4:7 back into the linked equations fails to reproduce the original ratios.

Option D:
Option D, 5:7, is another arbitrary-looking pair that does not emerge from the algebraic derivation. Computing a + b and b + c explicitly shows that their ratio is 16:21, not 5:7, so this option is inconsistent with the calculation.