Question

The average weight of boys in a class is 56 kg and the average weight of girls in the same class is 41 kg. If the average weight of the whole class is 47.25 kg. Number of girls constitutes what percent of the total number of students in the class ?

Answer 1

Given:

Average weight of boys  = 56 kg

Average weight of girls = 41 kg

Average weight of the whole class = 47.25 kg

To Find:

What percent of the total number of students in the class  does number of girls constitutes ?

Solution:

• Let N1 be the number of boys.

• Let N2 be the number of girls.

• Total number of students = N1+N2
• Total Weight Of Boys = N1 x 56
• Total Weight Of Girsl = N2 x 41
• Total Weight Of Class = 56N1 + 41N2
• Average Weight Of Class = (56N1+41N2) / (N1 + N2) = 47.25Kg

To Find the percentage of girls,

• N2/N1+N2 = $\frac{\frac{N2}{N1} }{1+ \frac{N2}{N1} }$ x 100

Now,

• Let N2/N1 = x
• (56 + 41x)/ ( 1+x) = 47.25
• 56 + 41x = 47.25 + 47.25x
• 8.75 = 6.25x
• x = 1.4

The Percentage of girls :

• x/(1+x) = 1.4/2.4 x 100 = 58.3%

Number of girls constitutes 58.3% of the total number of students in the class.