Test Index

Ratio and Proportion

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Question : 109 of 112

Marks: +1, -0

If

\;\frac{a}{3}= \;\frac{b}{4}= \;\frac{c}{5}

\;\frac{2 a+3 b+2 c}{4 a-b+2 c}

is

$\;\frac{11}{19}$
$\;\frac{17}{9}$
$\;\frac{14}{9}$
$\;\frac{19}{7}$

Solution:

Concept:

Use a common variable to express all terms in the ratio.

Explanation:

Let

\frac{a}{3} = \frac{b}{4} = \frac{c}{5} = k

.

Then

a = 3k

,

b = 4k

,

c = 5k

.

Substitute into

\frac{2a + 3b + 2c}{4a - b + 2c}

:

Numerator:

2(3k) + 3(4k) + 2(5k) = 6k + 12k + 10k = 28k

.

Denominator:

4(3k) - 4k + 2(5k) = 12k - 4k + 10k = 18k

.

Thus

\frac{28k}{18k} = \frac{28}{18} = \frac{14}{9}

.

Answer:

\frac{14}{9}

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