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If a ∶ b = 2 ∶ 3, then what is the value of (b2 + 2a2) ∶ (b2 - 2a2)?

If a ∶ b = 2 ∶ 3, then what is the value of (b2 + 2a2) ∶ (b2 - 2a2)? Correct Answer 17 ∶ 1

Given;

a : b = 2 : 3

Concept:

If a : b = x : y then,

a = bx/y

Calculation:

⇒ a : b = 2 : 3

⇒ a = 2b/3

⇒ (b2 + 2a2) ∶ (b2 - 2a2)

⇒ {b2 + 2 × (2b/3)2} : {b2 - 2 × (2b/3)2}

⇒ (9b2 + 8b2)/9 : (9b2 - 8b2)/9

⇒ 17b2/b2 = 17/1 = 17 : 1

∴ The required result will be 17 : 1.

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