Question

The average weight of students in a class is 67 kg. If the average weight of the boys in the class is 69 kg, and the number of boys is thrice the number of girls, what is the average weight of girls ?

Answer 1

Let the no. of the girls in the classroom = x
     then,   no. of boys in the classroom = 3x
Consider the total Wt. of girls = G
 and total Wt of boys = B
a/q,
       Average Wt of the students = 67 Kg
⇒ Total wt of student ÷ total no. of student = 67
⇒ (G+B)÷(x+3x) = 67
or, $\frac{G+B}{4x} =67$
or, G+B = 268x  -----------------(1)
And,
         average Wt of boys = 69
   ⇒  total Wt of boys ÷ total no. of boys = 69
  $or, \frac{B}{3x} = 69$
⇒     B = 207x  ----------(2)
put the value of  B in (1)
    G = 61x
⇒ $\frac{G}{x} =61$
therefore average Wt of girls = G ÷ x = 61 Kg

Answer 2

As ⇒ Average weight of students in a class
Ab ⇒ Avg. wt. of boys ;  Ag ⇒ Avg. wt. of girls
Ws ⇒ Total weight of the students in a class
Wb ⇒ Total weight of the boys ;  Wg ⇒ Total weight of the girls
Ns ⇒ Total no. of students in a class
Nb ⇒ No. of boys ;  Ng ⇒ No. of girls

Solution:
As = Ws / Ns = (Wb + Wg) / (Nb + Ng)  -------- Eq. 1
Ab = Wb / Nb
⇒Wb = Ab x Nb
   Wb = 69 x (3 x Ng) = 207 Ng --------- Eq. 2
Ag = Wg / Ng
⇒Wg = Ag x Ng ------------Eq. 3
On substituting Eq.s 2 and 3 in E. 1 , we get:
As =( (207 x Ng) + (Ag x Ng)) / ((3 x Ng) + Ng)
67 = ( (207 Ng) + (Ag x Ng)) / 4 Ng
(67 x 4 Ng) = (207 Ng) + (Ag x Ng)
268 Ng = (207 Ng) + (Ag x Ng)
Ag x Ng = 61 Ng
Ag = 61
Hence, the average weight of the girls in the class is 61 kg