Question

Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all the families together, there are more adults than boys, more boys than girls, and more girls than families, then the minimum possible number of families in the locality is

Answer 1

Answer:

3

Step-by-step explanation:

Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all the families together, there are more adults than boys, more boys than girls, and more girls than families, then the minimum possible number of families in the locality is

Let say Number of Families = F

Number of ADULTS  ≤ 2F

Number of children ≥ 3F

Number of children = Boys + Girls

=> Boys + Girls ≥ 3F

Girls > F

Boys > Girls

Boys < Adults

=>  Boys < 2F

2F  > Boys > Girls  > F

for minimum possible families

Girls = F + 1

Boys = Girls + 1 = F + 2

Boys + Girls ≥ 3F =>  2F + 3 ≥ 3F =>  3   ≥ F

2F = Boys + 1 = F + 2 + 1 = F + 3

=> 2F = F + 3

=> F = 3

F = 3

3 Families

4 Girls

5 Boys

6 Adults