Test Index

Ratio and Proportion

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Question : 93 of 112

Marks: +1, -0

If

\frac{\sqrt{x+5}+\sqrt{x-16}}{\sqrt{x+5}-\sqrt{x-16}} = \frac{7}{3}

x

equals

10
20
30
40

Solution:

Concept:

Use cross-multiplication on the given ratio

\frac{a+b}{a-b}=\frac{7}{3}

to relate

a

and

b

, then back-substitute and solve.

Explanation:

Let

a=\sqrt{x+5}

and

b=\sqrt{x-16}

.

Given

\frac{a+b}{a-b}=\frac{7}{3}

.

Cross multiply:

3(a+b)=7(a-b)

.

Expand:

3a+3b=7a-7b

.

Bring like terms:

3b+7b=7a-3a

.

Simplify:

10b=4a

, so

5b=2a

.

Substitute back:

5\sqrt{x-16}=2\sqrt{x+5}

.

Square both sides:

25(x-16)=4(x+5)

.

Expand:

25x-400=4x+20

.

Solve:

25x-4x=20+400

→

21x=420

→

x=20

.

Verification:

\sqrt{20+5}=5

,

\sqrt{20-16}=2

, ratio

\frac{5+2}{5-2}=\frac{7}{3}

.

Answer:

x=20

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