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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 ?Options2134

Question

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 ?Options2134

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Solution

Let's denote the number of daughters by D D and the number of sons by S S .

  1. Each daughter has the same number of brothers as she has sisters.

    • A daughter has S S brothers.
    • A daughter has D−1 D - 1 sisters.
    • Therefore, S=D−1 S = D - 1 .

  2. Each son has twice as many sisters as he has brothers.

    • A son has D D sisters.
    • A son has S−1 S - 1 brothers.
    • Therefore, D=2(S−1) D = 2(S - 1) .

Now, we have two equations: S=D−1 S = D - 1 D=2(S−1) D = 2(S - 1)

Substitute S=D−1 S = D - 1 into the second equation: D=2((D−1)−1) D = 2((D - 1) - 1) D=2(D−2) D = 2(D - 2) D=2D−4 D = 2D - 4 4=D 4 = D

So, there are 4 daughters.

Now, substitute D=4 D = 4 back into the first equation: S=4−1 S = 4 - 1 S=3 S = 3

Therefore, there are 3 sons in the family. The correct option is 3.

This problem has been solved

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