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ICSEClass 10MathematicsRatio And Proportion04 Mark2024 Moderate

QQuestion

If \frac{(a+b)^3}{(a-b)^3}=\frac{64}{27}:

(a) Find \frac{a+b}{a-b}.

(b) Hence, using properties of proportion, find a : b.

Exam-ready answer • 04 Mark

Answer

(a) Given:

\frac{(a+b)^3}{(a-b)^3}=\frac{64}{27} \left(\frac{a+b}{a-b}\right)^3=\frac{4^3}{3^3}

Taking the cube root of both sides:

\frac{a+b}{a-b}=\frac{4}{3}

(b) Using the above proportion:

3(a + b) = 4(a − b)

⇒ 3a + 3b = 4a − 4b

⇒ 4a − 3a = 3b + 4b

⇒ a = 7b

⇒ a/b = 7/1

Therefore, a : b = 7 : 1.

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