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Question

In a school $$\displaystyle \frac{3}{7}$$ of the students are girls and the rest are boys $$\displaystyle \frac{1}{4}$$ of the boys are below ten years of age and $$\displaystyle \frac{5}{6}$$ of the girls are also below ten years of age. If the number of students above ten years of age is 500, then find the total number of students in the school


A
600
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B
1000
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C
900
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D
1100
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Solution

The correct option is B 1000
Let the total number of students in the school be x
Then Number of girls  $$\Rightarrow  \frac{3x}{7}$$
Number of boys $$\Rightarrow  x-\frac{3x}{7}=\frac{4x}{7}$$
Number of boys below ten years of age $$\Rightarrow \frac{1}{4}\times \frac{4x}{7}=\frac{x}{7}$$
Number of girls below ten years of age $$\Rightarrow \frac{5}{6}\times \frac{3x}{7}=\frac{5x}{14}$$
$$\therefore$$ Total number of students below 10 years of age $$\Rightarrow \frac{x}{7}+\frac{5x}{14}=\frac{7x}{14}=\frac{x}{2}$$
$$\therefore$$ Total number of students above 10 years of age $$\Rightarrow x-\frac{x}{2}=\frac{x}{2}$$
Given $$\displaystyle \frac{x}{2}=500\Rightarrow x=1000$$

Mathematics

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