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Question

The ratio of the number of boys and girls in a college is $$7 : 8$$. If the percentage increase in the number of boys and girls be $$20\%$$ and $$10\%$$ respectively, what will be the new ratio?


A
8:9
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B
17:18
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C
21:22
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D
Cannot be determined
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Solution

The correct option is C $$21 : 22$$
Originally, let the number of boys and girls in the college be $$7x$$ and $$8x$$ respectively. 

The percentage increase in the number of boys and girls is $$20\%$$ and $$10\%$$ respectively,

Their increased number is ($$120\%$$ of $$7x$$) and ($$110\%$$ of $$8x$$).

 $$\left ( \dfrac{120}{100}\times 7x \right )$$ and  $$\left ( \dfrac{110}{100}\times 8x \right )$$

=>  $$ \dfrac{42x}{5}$$ and $$\dfrac {44x} {5} $$

$$\therefore$$ The required ratio = $$\left ( \dfrac{42x}{5}: \dfrac{44x}{5}\right )$$ $$= 21:22$$

Mathematics

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