Combining three ratios into one – UGC NET Question

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.