The average monthly income of A and B is $₹1400$, that of B and C is $₹1560$ and of A and C is $₹1440$. The monthly income of C is

Given the average incomes, we can write the sum of their incomes as follows:
1. $\frac{A+B}{2}=1400⟹A+B=2800$
2. $\frac{B+C}{2}=1560⟹B+C=3120$
3. $\frac{A+C}{2}=1440⟹A+C=2880$

Adding all three equations:

$$(A+B)+(B+C)+(A+C)=2800+3120+2880$$

$$2(A+B+C)=8800$$

$$A+B+C=4400$$

To find the monthly income of C, subtract the value of $(A+B)$ from $(A+B+C)$:

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

$$C=4400-2800$$

$$C=1600$$

Thus, the monthly income of C is $₹1600$.