Question : The ratio of the number of boys and girls in a school is 3 : 4 respectively. If the number of boys increases by 10% and the number of girls increases by 15%, what will be the new ratio of the number of boys to the number of girls?
Option 1: $\frac{33}{45}$
Option 2: $\frac{35}{46}$
Option 3: $\frac{33}{46}$
Option 4: $\frac{46}{33}$
Correct Answer: $\frac{33}{46}$
Solution :
Let the no. of boys and girls be $3x$ and $4x$ respectively.
Increase in no. of boys
$B = 3x(1 + 10\%)$
⇒ $ B = 3x(1 + 0.1)$
⇒ $ B = 3x(1.1) = 3.3x$
Increase in no. of girls
$G = 4x(1 + 15\%)$
⇒ $G = 4x(1 + 0.15)$
⇒ $G = 4x(1.15) = 4.6x$
New ratio of boys : girls = $\frac{3.3x}{4.6x}$
$= \frac{33}{46}$ or $33 : 46$
∴ The new ratio of the number of boys to the number of girls is $\frac{33}{46}$.
Hence, the correct answer is $\frac{33}{46}$.
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