Question

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

Answer 1

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 : (b^3/2)²

⇒ ((√a)3)² : ((√b)³)²

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