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 ?

A. 1300

B. 1500

C. 1600

D. Cannot be determined

E. None of these

Answer: Option E

Solution(By Examveda Team)

Let the number of boys and girls be 4x and 5x respectively.
Then,
$$\eqalign{ & {\text{ = }}\frac{{4x}}{{5x - 100}} = \frac{6}{7} \cr & \Rightarrow 28x = 30x - 600 \cr & \Rightarrow 2x = 600 \cr & \Rightarrow x = 300 \cr & \therefore {\text{Number of boys}} \cr & = 4 \times 300 \cr & = 1200 \cr} $$