Discussion
Match List I with List II.
| List I | List II |
|---|---|
| a. 3rd proportion to 16 and 32 is | I. 21 |
| b. 3rd proportion to 6 and 18 is | II. 54 |
| c. 4th proportion to 3, 7 and 9 is | III. 64 |
| d. 4th proportion to 4, 16 and 7 is | IV. 28 |
Choose the most appropriate answer from the options given below:
Answer: C
The correct matching is a-III, b-II, c-I, d-IV.
The third proportional to \(a\) and \(b\) is \(b^2/a\); the fourth proportional to \(a, b, c\) is \(bc/a\).
\[ \begin{aligned} \text{a: } 32^2/16 &= 64 \\ \text{b: } 18^2/6 &= 54 \\ \text{c: } 7 \times 9/3 &= 21 \\ \text{d: } 16 \times 7/4 &= 28 \end{aligned} \]
So a goes with 64 (III), b with 54 (II), c with 21 (I) and d with 28 (IV). Option A swaps b and c, giving 6 and 18 a third proportional of 21, which does not satisfy \(6 : 18 = 18 : x\).
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