Question 59

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

Solution

From the first condition: each daughter has the same number of brothers as she has sisters, let us assume the same number to be x.

So, no. of brothers = no. of sons = x

No. of daughters = x+1

Now, from the second condition, each son has twice as many sisters as he has brothers, we can say x+1=2(x-1)

Since each son will have x-1 brothers and x+1 sisters

So, x+1=2x-2

or, 1+2=2x-x

or, x=3

So, number of sons = x = 3

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