A family, each daughter has the same number of brothers as she has sister and each son has twice as many sisters as he has brothers. How many sons are there in the family?

Question

Answer

Solution:

Let's assume that there are x number of sons and y number of daughters in the family.

Number of brothers and sisters:

Each daughter has (y - 1) sisters and x brothers.
Each son has y sisters and (x - 1) brothers.

Using the given conditions:

Each daughter has the same number of brothers as she has sisters.
So, y - 1 = x
x = y - 1

Each son has twice as many sisters as he has brothers.
So, y = 2(x - 1)
y = 2x - 2

Substituting x = y - 1 in the above equation, we get:
y = 2(y - 1) - 2
y = 2y - 4
y = 4

Substituting y = 4 in x = y - 1, we get:
x = 3

Therefore, there are 3 sons in the family.

Explanation:

To solve this problem, we first assumed that there are x number of sons and y number of daughters in the family. Then we calculated the number of brothers and sisters for each daughter and son. Using the given conditions, we formed two equations and solved them simultaneously to find the values of x and y. Finally, we substituted the value of y in x = y - 1 to get the number of sons in the family.

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