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There are total 600 students in a school. Average age of boys is 12 years and of girls is 11 years while average age of all students is 11 yrs. And 9 months. Find the number of girls in the school.
- a)130
- b)140
- c)150
- d)160
- e)120
Correct answer is option 'C'. Can you explain this answer?
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Given:
Total number of students = 600
Average age of boys = 12 years
Average age of girls = 11 years
Average age of all students = 11 years and 9 months
To find:
Number of girls in the school
Solution:
Let the number of boys be B and the number of girls be G.
So, B + G = 600 (Total number of students)
From the given information,
Average age of boys = 12 years
So, sum of ages of all boys = 12B
Average age of girls = 11 years
So, sum of ages of all girls = 11G
Average age of all students = 11 years and 9 months
So, sum of ages of all students = 11.75(600) = 7050
Now we can write an equation based on the above information:
12B + 11G = 7050 (Sum of ages of all students)
Substituting B + G = 600, we get:
12B + 11(600 - B) = 7050
12B + 6600 - 11B = 7050
B = 450
Substituting B = 450, we get:
G = 600 - B = 150
Therefore, the number of girls in the school is 150.
Hence, option (c) is the correct answer.
Total number of students = 600
Average age of boys = 12 years
Average age of girls = 11 years
Average age of all students = 11 years and 9 months
To find:
Number of girls in the school
Solution:
Let the number of boys be B and the number of girls be G.
So, B + G = 600 (Total number of students)
From the given information,
Average age of boys = 12 years
So, sum of ages of all boys = 12B
Average age of girls = 11 years
So, sum of ages of all girls = 11G
Average age of all students = 11 years and 9 months
So, sum of ages of all students = 11.75(600) = 7050
Now we can write an equation based on the above information:
12B + 11G = 7050 (Sum of ages of all students)
Substituting B + G = 600, we get:
12B + 11(600 - B) = 7050
12B + 6600 - 11B = 7050
B = 450
Substituting B = 450, we get:
G = 600 - B = 150
Therefore, the number of girls in the school is 150.
Hence, option (c) is the correct answer.
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