Equal repeated ratios forming compound ratio – UGC NET Question

From a:b = 2:3, b:c = 2:3 and c:d = 2:3, we can write a/b = 2/3, b/c = 2/3 and c/d = 2/3. The compound ratio a:d is obtained by multiplying these three fractions: (2/3) × (2/3) × (2/3) = 8/27. Thus, a:d = 8:27.

Option A:
Option A, 2:3, uses only one of the three ratios and ignores the repeated multiplication required to go from a to d. It would be correct if we moved only one step in the chain, but we actually move through b and c as intermediate terms, so 2:3 is incomplete.

Option B:
Option B is correct because it cubes both numerator and denominator of the base ratio 2:3, reflecting the three links in the chain from a to d. The calculation (2/3)³ = 8/27 correctly captures the effect of applying the same proportional change three times in succession.

Option C:
Option C, 4:9, corresponds to squaring the base ratio, which would be appropriate if we had only two equal steps instead of three. Since there are three equal ratios a:b, b:c and c:d, 4:9 underestimates the cumulative effect.

Option D:
Option D, 16:81, arises from raising 2:3 to the fourth power and would require four equal proportional steps, which are not present in the given information. Therefore 16:81 overstates the change and does not match the structure of the problem.