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If \(\dfrac{a}{b}=\dfrac{2}{3}\), then the value of 5a3 - 2a2b ∶ 3ab2 - b3 is:
1. 32 ∶ 29
2. 16 ∶ 27
3. 27 ∶ 16
4. 34 ∶ 19

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Correct Answer - Option 2 : 16 ∶ 27

Given:

\(\dfrac{a}{b}=\dfrac{2}{3}\)

Calculation:

Let the value of A be 2x

And the value of B be 3x

According to the question:

5a3 - 2a2b ∶ 3ab2 - b3

 [5 × (2x)3 - 2 × (2x)2 × 3x : [3 × 2x × (3x)2 - (3x)3]

(5 × 8x3 - 2 × 4x2 × 3x) : (3 × 2x × 9x2 - 27x3)

⇒ (40x3 -  24x3) : (54x3 - 27x3)

⇒ 16x3 : 27x3 = 16 : 27

∴ The answer will be 16 : 27.

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