Problem : How many brothers and sisters are there?

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A family I know has several children. Each boy in this family has as many sisters as brothers but each girl has twice as many brothers as sisters. How many brothers and sisters are there?

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Let B be the number of boys and G be the number of girls in the family.

As each boy in the family has same number of sisters which gives the below 

equation since we have to exclude each of the boys while correlating brother-sister relationship, we get

B-1 = G —————————(1)

Second condition says that Each girl in the family has twice the number of brothers as sisters which gives

2(G-1) = B ————————(2)

Solving (1) and (2) we get B = 4 and G = 3 which gives 4 brothers and 3 sisters in the family.

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