Test Index

Ratio and Proportion

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Question : 105 of 112

Marks: +1, -0

For

a, b, c>0

the value of each ratio is

\; \frac{a}{b+c} = \; \frac{b}{c+a} = \; \frac{c}{a+b}

then find the value of each ratio if

a+b+c \neq 0

$\frac{1}{2}$
$\frac{1}{3}$
$\frac{1}{4}$
1

Solution:

Concept:

Set each equal ratio to a common variable

k

and then sum the resulting equations.

Explanation:

Let

\frac{a}{b+c} = \frac{b}{c+a} = \frac{c}{a+b} = k

.

Then

a = k(b+c)

,

b = k(c+a)

,

c = k(a+b)

.

Add the three equations:

a+b+c = k[(b+c)+(c+a)+(a+b)] = k[2(a+b+c)]

.

Since

a+b+c \neq 0

, divide both sides by

a+b+c

to get

1 = 2k

.

Thus

k = \frac{1}{2}

.

Answer:

\frac{1}{2}

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