Find Q in the addition
$\begin{array}{c}31Q\\ +1Q3\\ 501\end{array}$

The correct option is D

8

There is just one letter Q whose value we have to find.

Study the addition in the ones column: from Q+ 3, we get '1', that is, a number whose ones digit is I.

For this to happen, the digit Q should be 8. So the puzzle can be solved as shown below.

$\begin{array}{c}31Q\\ +1Q3\\ 501\end{array}$ That is, Q = 8
Alternatively, the question can be solved using algebra as:
At hundred's place , the sum is 5 while the terms being added are 3,1. As 3+1=4, 1 is carried over from the sum of ten's place
Now, considering the sum of ones and ten's digits, 10 + 10Q + Q + 3 = 101 ( Considering 1 as the carry over from the ten's place )
$\Rightarrow$ 13 + 11Q=101
$\Rightarrow$ 11Q=88
$\Rightarrow$ Q=8.