Question

The mean height of 45 students is 152cm. If the mean height of girls alone is 144cm and that of boys alone is 168cm. Find the number of boys and girls in the class

Answer 1

g = number of girls

b = number of boys

SG = Sum of height of all girls

SB = Sum of height of all boys

There are 45 studentss in the class.

g = 45 - b

The mean height of girls:

Sum of height of all girls / g = 144

SG / g = 144

SG = 144 ∙ g

SG = 144 ∙ ( 45 - b )

SG = 6480 - 144 b

The mean height of boys:

Sum of height of all boys / b = 168 cm

SB / b = 168

SB = 168 b

The mean height of 45 students is 152cm.

( SG + SB ) / 45 = 152

( 6480 - 144 b + 168 b ) / 45 = 152

6480 + 24 b = 45 ∙ 152

6480 + 24 b = 6840

24 b = 6840 - 6480

24 b = 360

b = 360 / 24

b = 15

g = 45 - b = 45 - 15 = 30

There are 30 girls and 15 boys in the class.