216 = n*x
216 = (n+6)*(x-3)

x = 216/n

216 = (n + 6)(216/n - 3)

slove equation and get the number of children

sumitrajsaxena wrote:Kindly see the following problem of quant PS.

A bag of 216 caramels is divided equally among a group of children. If 6 children were added to the group, each child would receive 3 fewer caramels. How many children are in the group?

You could also look at the factors of 216: look for two that differ by 6 and whose quotients differ by 3.

216= 6^3 =2^3 x 3^3

18 x 12 , 24 x 9

18 children , 12 caramels each
24 children, 9 caramels each

Let us say the group of children = N

given 216/N caramels per child

when 6 more children have been added
216/(N+6)

216/N-3 = 216/(N+6) [ subtract 3 from the initial per child caramel count to get the new per child caramel count]

216/N-216/(N+6) = 3

there are two ways you can solve this now

1) solve for N^2+6N-216 =0
givens two values = -24,18

2) if values are provided in the question substitute the values.

Thanks guys for detailed explanations. I got it now.