Question : In a school, there were 1554 students, and the ratio of boys to girls was 4 : 3. After a few days, 30 girls joined the school but a few boys left. As a result, the ratio of boys and girls became 7 : 6. The number of boys who left the school is:
Option 1: 76
Option 2: 74
Option 3: 84
Option 4: 86
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Correct Answer: 76
Solution :
Total students = 1554
The ratio of the boys and girls = 4 : 3
According to the given information,
The number of boys = $\frac{4}{4+3}×1554$ = 888
and, the number of girls = $\frac{3}{4+3}×1554$ = 666
After a few days, 30 girls joined and a few boys left.
The new number of girls = 666 + 30 = 696
Let $x$ boys leave the school.
So, the new number of boys = 888 - $x$
Now, according to the question
$(\frac{888-x}{696})=\frac{7}{6}$
⇒ $(\frac{888-x}{116})=7$
⇒ $(888-x)=116×7=812$
⇒ $x=(888-812)=76$
Hence, the correct answer is 76.
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