Team $A$ consists of $7$ boys and $n$ girls and Team $B$ has $4$ boys and $6$ girls. If a total of $52$ single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then $n$ is equal to

The correct option is D

$4$

Explanation for the correct option:

Find the number of girls in the team $A$:

Number of single matches that can arranged between Team $A$ and Team $B$ boys $=7\times 4$

$=28$

Number of single matches that can arranged between Team $A$ and Team $B$ girls $=n\times 6$

$=6n$

Therefore, the total number of single matches arranged between two teams when a boy plays against a boy and a girl plays against a girls $=28+6n$

$$\begin{gathered} \Rightarrow 28+6n=52 \\ \Rightarrow 6n=24 \\ \Rightarrow n=4 \end{gathered}$$

Therefore, the number of girls in the Team $A$$=4$

Hence, option (D) is the correct answer.