Question

here are 40 boys in a class. one boy weighing 40 kg goes away and at the same time another boy joins the class. if the average weight of the class is thus increased by 100 gm the weight of the new boy is

Answer 1

Let m be the mass of the part of the class that doesn't change. Let x be the mass of the new boy. 

The initial average mass (A_i) with the 40kg boy is: (total mass divided by the number of boys) 
A_i = (m+40)/40 = m/40 + 1 

The final average mass with the new boy is: 
A_f = (m+x)/40 = m/40 + x/40 

The change in average mass is 
A_f - A_i = m/40 + x/40 - (m/40 + 1) = x/40 - 1 

I assume you meant 100 g (g is the abbreviation for grams). This equals 0.1 kg. 

The average increased by 0.1 kg so: 
x/40 - 1 = 0.1 
x/40 = 1.1 
x = 44 

The new boy has a mass of 44 kg