In a family there are several brothers and sisters. Every 2 boys have brothers as many as sisters and each girl has 2 brothers less than twice as many brothers as sisters. Now find the number of boys and girls.

Solution (By Examveda Team)

Let B be the number of brothers and S be the number of sisters in the family.

Step 1: Understanding the condition for the boys
If we pick any 2 boys, they will have (B - 2) other brothers (excluding themselves).
According to the question, this number is equal to the number of sisters they have.
So, we get:
B - 2 = S
Rewriting this:
B - S = 2 ............(1)

Step 2: Understanding the condition for the girls
Each girl has (S - 1) sisters (excluding herself).
Twice the number of sisters = 2(S - 1)
Each girl has 2 brothers less than that:
So, number of brothers B = 2(S - 1) - 2
Simplifying:
B = 2S - 4 ............(2)

Step 3: Solving the equations
Now, substitute equation (2) into equation (1):
(2S - 4) - S = 2
2S - 4 - S = 2
S = 6

Now substitute S = 6 back into equation (1):
B - 6 = 2
B = 8

Final Answer:
There are 8 boys and 6 girls in the family.

Correct Option: A) 8 , 6