There are two possible answers:
Answer1: Number of children = 14, Ladies= 5 and Gents = 1
Answer2: Number od children = 16, Ladies = 0 and Gents = 4.
How?
We can form the mathematical equations and solve them, lets assume number of children = x, ladies = y and gents = z.

Then we can form these two equations

1. x + y + z = 20(Total number of people in family)
2. x/2 + 2y + 3z = 20 (Total number of chapati’s)

Now we can solve above two equations as below

x/2 + 2(y+z) + z = 20
x/2 + 2(20 -x) + z = 20 (replaced y+z from first equation)
40 + z -3x/2 = 20
3x/2 = 20 +z
as z > 0 => 3x/2 > 20, x = 14, 16, 18...

We can see that y becomes negative for any value of x greater than or equal to 18,thus x = 14 and 16 are two possible values. we can get the corresponding values of y and z as well.

Answer is 120.
How?
If we observe
10 = 2×5
30 = 3×10
So every next result = multiplication of first number and previous result. thus the answer to above number puzzle should be 4×30 = 120.