How many Child, Ladies and Gents are there in the family?

Question

One family of 20 members have 20 chapatis to eat, finally

Every child gets 1/2 chapati
Every Lady in the house gets 2 chapatis
And every gentleman gets 3 chapatis to eat.

How many Child, Ladies and Gents are there in the family?

Answer 1

Lets assume number of children are X
number of ladies are Y
number of gents are Z

Now
X+Y+Z = 20 ;
1/2 x + 2 Y + 3 Z = 20 ;
and X,Y,Z are integers and greater then or equal to zero.

Now we can deduce -
X is even
y < 10 and Z < 6

Now try trial and error after removing one variable from able two equations (i.e. 3y+5z = 20) which gives as y=0 & z=4 and y=5 & z=1. Second solution fits in the above equations so

number of children X = 14
number of ladies Y = 5
number of gents Z = 1

Answer 2

Gentlemen = 1
Women = 5
Child = 14

Answer 3

14 childrens=7 chapatis
5ladies=10 chapatis
1man=3 chapatis

Answer 4

14 child, 5 ladies, 1 gents