Test Index

Ratio and Proportion

Question : 53 of 112

Marks: +1, -0

Solution:

Concept:

The sum of a ratio and its reciprocal is always at least

2

Explanation:

Let the number of boys be

b

and girls be

g

, where both are positive.

Then

B = \frac{b}{g}

and

G = \frac{g}{b}

B + G = \frac{b}{g} + \frac{g}{b} = \frac{b^2 + g^2}{bg}

By the AM–GM inequality,

b^2 + g^2 \ge 2bg

, with equality only when

b = g

Therefore

B + G \ge 2

Since

2

is greater than

1

B + G

is always greater than

1

Answer:

Option B: greater than

1

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