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Ratio and Proportion

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Question : 59 of 112

Marks: +1, -0

The number has same ratio to

\frac{7}{33}

\frac{8}{21}

\frac{4}{9}

$\frac{2}{11}$
$\frac{3}{11}$
$\frac{2}{21}$
None

Solution:

Concept:

Given that the unknown number

x

and

\frac{7}{33}

are in the same ratio as

\frac{8}{21}

and

\frac{4}{9}

.

Explanation:

Set up the proportion:

x : \frac{7}{33} = \frac{8}{21} : \frac{4}{9}

.

This means

\frac{x}{\frac{7}{33}} = \frac{\frac{8}{21}}{\frac{4}{9}}

.

Simplify the right-hand side:

\frac{8}{21} \div \frac{4}{9} = \frac{8}{21} \times \frac{9}{4} = \frac{72}{84} = \frac{6}{7}

.

Simplify the left-hand side:

\frac{x}{\frac{7}{33}} = x \times \frac{33}{7} = \frac{33x}{7}

.

Equate both sides:

\frac{33x}{7} = \frac{6}{7}

.

Multiply both sides by

7

:

33x = 6

.

Solve for

x

:

x = \frac{6}{33} = \frac{2}{11}

.

Answer:

The number is

\frac{2}{11}

, which corresponds to option A.

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