If the ratio of boys to girls in a class is B and the ratio of girls t

1.	If the ratio of boys to girls in a class is B and the ratio of girls to boys is G, then B+G is ………A) greater than 1 or equal to 1B) greater than 1 C) less than 1 D) equal to 1
Answer» Correct option is (B) greater than 1 Let there are x number of girls and y number of boys in the class. The ratio of boys to girls in the class is B. \(\therefore\) \(\frac xy\) = B _________(1) The ratio of girls to boys in the class is G. \(\therefore\) \(\frac yx\) = G _________(2) Now, B+G \(=\frac xy+\frac yx\) \(=\frac{x^2+y^2}{xy}\) \(\because(x-y)^2\geq0\) \(\Rightarrow x^2+y^2-2xy\geq0\) \(\Rightarrow x^2+y^2\geq2xy\) \(\Rightarrow\frac{x^2+y^2}{xy}\geq2>1\) \(\Rightarrow\frac{x^2+y^2}{xy}>1\) Hence, B+G > 1 Correct option is(B) greater than 1

If the ratio of boys to girls in a class is B and the ratio of girls to boys is G, then B+G is ………A) greater than 1 or equal to 1B) greater than 1 C) less than 1 D) equal to 1

Answer»

Correct option is (B) greater than 1

Let there are x number of girls and y number of boys in the class.

The ratio of boys to girls in the class is B.

\(\therefore\) \(\frac xy\) = B _________(1)

The ratio of girls to boys in the class is G.

\(\therefore\) \(\frac yx\) = G _________(2)

Now, B+G \(=\frac xy+\frac yx\)

\(=\frac{x^2+y^2}{xy}\)

\(\because(x-y)^2\geq0\)

\(\Rightarrow x^2+y^2-2xy\geq0\)

\(\Rightarrow x^2+y^2\geq2xy\)

\(\Rightarrow\frac{x^2+y^2}{xy}\geq2>1\)

\(\Rightarrow\frac{x^2+y^2}{xy}>1\)

Hence, B+G > 1

Correct option is(B) greater than 1