Question : In a school with 600 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years and 9 months, then the number of girls in the school is:
Option 1: 450
Option 2: 150
Option 3: 250
Option 4: 350
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Correct Answer: 150
Solution :
Average of boys = 12 years
Average of girls = 11 years
Average of all students = 11 years 9 months
By using alligation, we get:
Total students = 600
Girls = 12 years – 11 years 9 months = 3 months
Boys = 11 years 9 months – 11 years = 9 months
So, Boys : Girls = 9 : 3 = 3 : 1
$\therefore$ Number of girls = $\frac{1}{4}$ × 600 = 150
Hence, the correct answer is 150.
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