Question

Dheeraj has twice as many sisters as he has brothers. If Deepa, Dheeraj’s sister has the same number of brothers as she has sisters, then how many brothers does Deepa have?
(a) 2
(b) 3
(c) 4
(d) Cannot be determined

Answer 1

Hint: We solve this problem by assuming that the total number of boys and total number of girls in the given family as two variables. Then we can form two equations of two variables from the given two conditions so that we can solve for required value.
We need to keep in mind that while talking about the number of brothers of a boy we don’t consider him into the count of brothers similarly for the girls.

Complete step by step answer:
Let us assume that the total number of boys in Deeraj’s family as \['x'\]
Let us assume that the total number of girls in Deeraj’s family as \['y'\]
We are given that Dheeraj has twice as many sisters as he has brothers
We know that if we take the count of brothers of boys in a family we don’t consider him into count.
So, we can say that Dheeraj has \[x-1\] brothers and \[y\] sisters.
Now, by converting the given statement into mathematical equation we get
\[\begin{align}
  & \Rightarrow y=2\left( x-1 \right) \\
 & \Rightarrow 2x-2=y.........equation(i) \\
\end{align}\]
Now, let us take the second statement
We are given that Deepa, Dheeraj’s sister has the same number of brothers as she has sisters
Here, we can see that the statement is considered with respect to a girl Deepa.
We know that if we count the number of sisters of a girl in a family then we don’t consider her in the count.
So, we can say that Deepa has \[x\] brothers and \[y-1\] sisters.
Now, by converting the given statement into mathematical equation we get
\[\begin{align}
  & \Rightarrow y-1=x \\
 & \Rightarrow y=x+1........equation(ii) \\
\end{align}\]
Now, by substituting the equation (ii) in equation (i) we get
\[\begin{align}
  & \Rightarrow 2x-2=x+1 \\
 & \Rightarrow x=3 \\
\end{align}\]
Therefore, Deepa has \[x\] brothers which is equal to 3
So, we can conclude that Deepa has 3 brothers.

So, the correct answer is “Option b”.

Note: We need to note that if we take the count of brothers of boys in a family we don’t consider him.
Therefore we get the mathematical form of first equation as
\[\begin{align}
  & \Rightarrow y=2\left( x-1 \right) \\
 & \Rightarrow 2x-2=y \\
\end{align}\]
But students may miss this point and take the mathematical equation of first statement as
\[\Rightarrow y=2x\]
This gave the wrong answer because while taking the count of brothers of boys in the family we count the number of brothers he has. On that count we don’t consider him because a person cannot be a brother to himself.
Similarly a girl cannot be a sister to herself.
Keeping these two points in the mind we get the correct answer.