# THE MEAN WEIGHT OF 150 STUDENTS IN A CLASS IS 60 KG.THE MEAN WEIGHT OF BOYS IN THE CLASS IS 70 KG AND THAT OF GIRLS IS 55 KGS.FIND THE NUMBER OF GIRLS IN THE CLASS.

Let the number of boys be = x

Let the number of girls be = y

total students in the class = 150

Therefore ,

x + y = 150 ----------(1)

Now

mean weight of boys(x̄

_{1}) = 70

mean weight of girls(x̄

_{2})= 55

Combined mean weight of 150 students(x̄

_{c}) = 60

therefore , by combined arithmetic mean method, we get,

x̄

_{1}× x + x̄

_{2}× y / 150 = 60

x̄

_{1}x +x̄

_{2}y = 60 ---------(2)

Solving equations (1) and (2) we get,

x = 50 and y = 100

now number of girls are = y = 100

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