Question

An old man said to a young man, "I have a daughter. She has as many brothers as she has sisters. Each one of her brothers has twice as many sisters as he has brothers. How many sons and daughters do I have?"

Answer 1

4 daughters and 3 sons
4-1=3
3-1=2*2

Answer 2

Say
Total number of sons = x and
Total number of daughters = y

"She has as many brothers as she has sisters"
number of her sisters = y-1
So
x = y-1 -- (1)

"Each one of her brothers has twice as many sisters as he has brothers"
number of his brothers = x-1
number of his sisters 2(x-1)
So
y = 2(x-1) -- (2)

Substituting y value from (2) in (1)
x = 2(x-1) - 1 = 2x - 3
That is x = 3 and y = 4
Hence
Number of sons = 3
Number of daughters = 4