# The ratio of P and Q is the duplicate ratio of ratio of a : b. The ratio of Q and R is the sub duplicate ratio of P : Q. The ratio of P and R is the d

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The ratio of P and Q is the duplicate ratio of ratio of a : b. The ratio of Q and R is the sub duplicate ratio of P : Q. The ratio of P and R is the duplicate ratio of ________.
1. a2 : b2
2. √a : √b
3. (√a)3 : (√b)3
4. a3 : b3

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Correct Answer - Option 3 : (√a)3 : (√b)3

Given:

The ratio of P and Q is the duplicate ratio of a : b.

Concept used:

The duplicate ratio of a : b is a2 : b2.

The sub-duplicate ratio of a : b is √a : √b.

Calculation:

The given ratio is a: b.

P : Q = a2 : b2

Q : R = √(a)2 : √(b2

⇒ a : b

Step 1:

 P Q R a2 b2 a b

Step 2:

 P Q R a2 b2 b2 a a b

P : Q : R = a3 : ab2 : b3

Now P : R = a3 : b3

⇒ (a3/2)2 : (b3/2)2

⇒ ((√a)3)2 : ((√b)3)2

∴ The ratio of P : R is the duplicate ratio of (√a)3 : (√b)3.
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