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Select the correct answerIn 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 ?Options1342

Question

Select the correct answerIn 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 ?Options1342

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Solution

Let's solve this step by step:

  1. Let's assume the number of daughters in the family is 'd' and the number of sons is 's'.

  2. According to the problem, each daughter has the same number of brothers as she has sisters. This means that the number of brothers a daughter has is equal to the number of daughters minus one (since a girl is not a sister to herself). So, we can write this as: s = d - 1.

  3. The problem also states that each son has twice as many sisters as he has brothers. This means that the number of sisters a son has is twice the number of sons minus one (since a boy is not a brother to himself). So, we can write this as: d = 2(s - 1).

  4. Now we have two equations and two unknowns, so we can solve for 's' (the number of sons). Substituting the first equation into the second gives: d = 2((d - 1) - 1), which simplifies to: d = 2d - 4.

  5. Solving for 'd' gives: d = 4. Substituting d = 4 into the first equation gives: s = 4 - 1 = 3.

So, there are 3 sons in the family. The correct answer is 3.

This problem has been solved

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