Question : The ratio of boys and girls in a college is 5 : 3. If 50 boys leave the college and 50 girls join the college, the ratio becomes 9 : 7. The number of boys in the college is:
Option 1: 300
Option 2: 400
Option 3: 500
Option 4: 600
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Correct Answer: 500
Solution :
Boys : Girls = 5 : 3
Let the number of boys be $5x$ and the number of girls be $3x$.
According to the question,
If 50 boys leave and 50 girls join, the ratio becomes 9 : 7.
So, $\frac{5x-50}{3x+50} = \frac{9}{7}$
⇒ $7(5x - 50)=9(3x+50)$
⇒ $35x - 350 = 27x+450$
⇒ $35x-27x = 450+350$
⇒ $8x = 800$
⇒ $x=100$
$\therefore$ The number of boys is 5$x$ = 5 × 100 = 500
Hence, the correct answer is 500.
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