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Ratio and Proportion Practice Test 4

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Question : 13 of 40

Marks: +1, -0

If

(20x^2 + 7y^2) : (8y^2 + x^2) = 4 : 1

, then (x : y) is:

4 : 5
3 : 2
5 : 4
2 : 3
1 : 4

Solution:

Concept:

A ratio

a:b

can be written as

\frac{a}{b}

, so equate and solve.

Explanation:

Given

\frac{20x^2+7y^2}{8y^2+x^2}=\frac{4}{1}

.

Cross-multiply:

20x^2+7y^2=4(8y^2+x^2)

.

Expand:

20x^2+7y^2=32y^2+4x^2

.

Rearrange:

16x^2=25y^2

.

So

\frac{x^2}{y^2}=\frac{25}{16}

.

Taking positive square roots:

\frac{x}{y}=\frac{5}{4}

.

Therefore

x:y=5:4

.

Answer:

x:y=5:4

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