Test Index

Ratio and Proportion

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Question : 103 of 112

Marks: +1, -0

For

p, q, r, s > 0

the value of each ratio is

\; \frac{P}{q+r} = \; \frac{q}{r+s} = \; \frac{r}{s+p} = \; \frac{s}{p+q} \; \;

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

Solution:

Concept:

Equal ratios property: The common ratio equals sum of numerators divided by sum of denominators.

Explanation:

Let the common value be

k

.

So,

k = \frac{p}{q+r} = \frac{q}{r+s} = \frac{r}{s+p} = \frac{s}{p+q}

.

Sum of numerators:

p+q+r+s

.

Sum of denominators:

(q+r)+(r+s)+(s+p)+(p+q) = 2(p+q+r+s)

.

Since all

p,q,r,s > 0

, denominators are positive.

Thus,

k = \frac{p+q+r+s}{2(p+q+r+s)} = \frac12

.

Answer:

\frac12

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