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In a school the ratio of boys and girls is 4 : 5 respectively. When 100 girls leave the school the ratio becomes 6 : 7 respectively. How many boys are there in the school ?
Answer & Solution
Correct Answer:
Option
E
Let the number of boys and girls be 4x and 5x respectively.
Then,
$$\eqalign{ & {\text{ = }}\frac{{4x}}{{5x - 100}} = \frac{6}{7} \cr & \Rightarrow 28x = 30x - 600 \cr & \Rightarrow 2x = 600 \cr & \Rightarrow x = 300 \cr & \therefore {\text{Number of boys}} \cr & = 4 \times 300 \cr & = 1200 \cr} $$
Then,
$$\eqalign{ & {\text{ = }}\frac{{4x}}{{5x - 100}} = \frac{6}{7} \cr & \Rightarrow 28x = 30x - 600 \cr & \Rightarrow 2x = 600 \cr & \Rightarrow x = 300 \cr & \therefore {\text{Number of boys}} \cr & = 4 \times 300 \cr & = 1200 \cr} $$
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