The average per day income of $A$, $B$ and $C$ is $\text{Rs. }45$. If the average per day income of $A$ and $B$ is $\text{Rs. }40$ and that of $B$ and $C$ is $\text{Rs. }43$, then the per day income of $B$ is:

Let the daily incomes of $A$, $B$, and $C$ be denoted by $A$, $B$, and $C$ respectively.
From the problem, we can set up the following equations based on total incomes:

$$A+B+C=45\times 3=135\text{— (Equation 1)}$$

$$A+B=40\times 2=80\text{— (Equation 2)}$$

$$B+C=43\times 2=86\text{— (Equation 3)}$$

Adding Equation 2 and Equation 3 together:

$$(A+B)+(B+C)=80+86$$

$$A+2B+C=166$$

$$(A+B+C)+B=166$$

Substituting the value from Equation 1 into the expression:

$$135+B=166$$

$$B=166-135=31$$

Thus, the per day income of $B$ is $\text{Rs. }31$.