Match List-I with List-II.
| List-I (Ratio) | List-II (Value) | ||
|---|---|---|---|
| (A) | Duplicate ratio of \(2:3\) | (I) | \(4:5\) |
| (B) | Sub-duplicate ratio of \(16:25\) | (II) | \(1:8\) |
| (C) | Triplicate ratio of \(1:2\) | (III) | \(1:2\) |
| (D) | Compound ratio of \(2:3\) and \(3:4\) | (IV) | \(4:9\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(IV), (B)-(I), (C)-(II), (D)-(III)
The duplicate ratio of \(a:b\) is \(a^2:b^2\), the sub-duplicate ratio is \(\sqrt{a}:\sqrt{b}\), the triplicate ratio is \(a^3:b^3\), and the compound ratio of \(a:b\) and \(c:d\) is \(ac:bd\).
(A) Duplicate ratio of \(2:3\) — this matches (IV) \(4:9\). \(2^2:3^2=4:9\).
(B) Sub-duplicate ratio of \(16:25\) — this matches (I) \(4:5\). \(\sqrt{16}:\sqrt{25}=4:5\).
(C) Triplicate ratio of \(1:2\) — this matches (II) \(1:8\). \(1^3:2^3=1:8\).
(D) Compound ratio of \(2:3\) and \(3:4\) — this matches (III) \(1:2\). \((2\times3):(3\times4)=6:12=1:2\).