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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