If $5A\times A=399$, then the value of $A$ is

The correct option is C

$7$

Explanation for the correct option

Option(C): Given that $5A\times A=399$

In the units place, the product of $A$ and $A$ gives $9$ $\Rightarrow A$can be $3$ or $7$

Here, $A$ is a number whose multiplication gives the two digit number having $9$ in its units place $\Rightarrow A$should be $7$

So, the product of $7$ and $7$ gives $49$, where units place is $9$

$\begin{array}{crcc}& 5A\times A& =& 399\\ \Rightarrow & 57\times 7& =& 399\\ \Rightarrow & 399& =& 399\end{array}$

$\Rightarrow$ L.H.S. $=$ R.H.S.

Thus option$\left(C\right)$ is correct

Explanation for incorrect options

Option(A):

$\begin{array}{crcc}& 5A\times A& =& 399\\ \Rightarrow & 53\times 3& =& 399\\ \Rightarrow & 159& \ne & 399\end{array}$

$\Rightarrow$ L.H.S. $\ne$ R.H.S.

Option(B):

$\begin{array}{crcc}& 5A\times A& =& 399\\ \Rightarrow & 56\times 6& =& 399\\ \Rightarrow & 336& \ne & 399\end{array}$

$\Rightarrow$ L.H.S. $\ne$ R.H.S.

Option(D):

$\begin{array}{crcc}& 5A\times A& =& 399\\ \Rightarrow & 59\times 9& =& 399\\ \Rightarrow & 531& \ne & 399\end{array}$

$\Rightarrow$ L.H.S. $\ne$ R.H.S.

Thus options$\left(A\right)$, $\left(B\right)$, $\left(D\right)$ are incorrect

Hence option (C) is correct i.e. $7$