The mean weight of 150 students in a class is 60 kg. The mean weight of boys is 70 kg and that of girls is 55 kg. What is the number of boys in the class?
A). 50
B). 60
C). 75
D). 100
Answers
Step-by-step explanation:
total students in class = 150
mean weight = 60 kg
total weight = 150×60 = 9000 kg
Let the total number of boys = x
mean weight of boys = 70kg
total weight of boys = 70×x = 70x kg
total number of girls = total students - no. of boys = 150 - x
mean weight of girls= 55kg
total weight of girls = 55×(150-x) = 55×150 - 55x = (8250 - 55x) kg
Total weight = weight of boys + weight of girls
⇒ 9000 = 70x + (8250 - 55x)
⇒ 9000 = 70x + 8250 - 55x
⇒ 9000 - 8250 = 70x - 55x
⇒ 750 = 15x
⇒ x = 750/15
⇒ x = 50
So number of boys = 50
number of girls = 150 - 50 = 100
Let the number of boys and girls be x and y respectively
x+y=150 .....(1)
The mean weight of 150 students in a class =60
Total weight =150×60=9,000 kg
The mean weight of boys=70kg
Total weight of boys=70x
The mean weight of girls=55kg
Total weight of girls=55y
70x+55y=9,000 kg
14x+11y=1800 ..(2)
Multipling equation (1) by 11, we get
11x+11y=1650 ...(3)
Subtract equation (3) from equation (2), we get
3x=150
x=50
substituting x=50 in education (1),we get
50+y=150
y=100
Hence, number of boys =50 and number of girls =100
Therefore, number of boys =50
Therefore, option( a) is correct