Question

A group of children share a box of 60

sweets equally.If each child were to
receive one sweet fewer,there would
be enough sweets left over for two
more children to receive the same
number as each child in the group originally received.how many children
are in the group?

Answer 1

number of children -- c

number of sweets per child -- s
sc = 60 or c = 60/s

2nd scenario:
number of sweets per child = s-1
(s-1)(c+2) = 60
sc+ 2s - c - 2 = 60
60 + 2s - c - 2 = 60
2s - c = 2
2s - 60/s = 2
2s^2 - 60 = 2s
s^2 - s - 30 = 0
(s+5)(s-6) = 0
s = 6 or s is a negative

if s = 6, then c = 60/6 = 10

so there were 10 children, each receiving 6 sweets

check:
2nd case, each child receives 5 sweets,
then 60/5 = 12 children , two more than the original number of children.

Not 100% sure if I interpreted the question correctly.