40 marbles are equally divided among a certain number of children. If there were 2 children less, each would have received 1 more marble. Find the number of children.

Soln:

Let number of children be x. 

Then each student will get 40/x

If there were 2 children less i.e x-2 then each would get 40/(x-2)

According to question

40/(x-2)-40/x = 1

[40*x-40*(x-2)]/[(x-2)x] = 1

(40x-40x+80)/(x^2-2x) = 1

x^2-2x-80 = 0

x^2-(10-8)x-80 = 0

x^2-10x+2x-20 = 0

x(x-10)+2(x-10) = 0

(x-10)(x+2) = 0

Either,                                

x-10 = 0 

x = 10

or, 

x+2 = 0

x = -2 (No. of marbles cannot be negative.)

Therefore, required number of marbles is 10.