The mean weight of 150 students in a class is 60 kg. The mean weight of the boys is 70 kg. while that of the
girls is 55 kg. Find the number of boys and that of the girls in the class respectively.
(A) 75.75
(B) 100.50 (C) 25.125
(D) 60.90
(E) 50.100
Answers
Let :
- Number of boys = x
- Number of girls = y
Given :
- Total number of students = 150
- Mean weight of students = 60kg
- Mean weight of boys = 70kg
- Mean weight of girls = 55kg
To find :
- Number of boys (x)
- Number of girls (y)
Formula used :
Average = Sum of observation ÷ Number of observation
Solution :
Total number of students = number of boys + number of girls
➝ 150 = x + y
➝ x = 150 - y equation 1
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Mean weight of students = sum of weight of all students ÷ Total number of students
➝ 60 = Sum of weight of all students ÷ 150
➝ Sum of weight of all students = 60 × 150
➝ Sum of weight of all students = 9000
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Mean weight of boys = Sum of weight of all boys ÷ Number of boys
➝ 70 = Sum of weight of all boys ÷ x
➝ Sum of weight of all boys = 70x
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Mean weight of girls = Sum of weight of all girls ÷ Number of girls
➝ 55 = Sum of weight of all girls ÷ x
➝ Sum of weight of all girls = 55y
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Sum of weight of all students = sum of weight of boys + sum of weight of girls
➝ 9000 = 70x + 55y equation 2
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Put value of x from equation 1 into equation 2
➝ 9000 = 70(150-y) + 55y
➝ 9000 = 10500 - 70y + 55y
➝ 9000 - 10500 = -15y
➝ - 1500 = -15y
➝ y = (-1500) ÷ (-15)
➝ y = 100
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Now put value of y in equation 1,
x = 150 - 100
x = 50
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Number of boys = 50
Number of girls = 100
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ANSWER :
Option E) 50,100