The ratio of income of two persons is $10:6$ and that of their expenditures is $18:10$. If they save ₹$5,200$ and ₹$3,600$ respectively, their incomes are:

Let the incomes of the two persons be $10x$ and $6x$, and their expenditures be $18y$ and $10y$.
Since $\text{Income}-\text{Expenditure}=\text{Savings}$, we can set up the following equations:

1. $10x-18y=5200⟹5x-9y=2600$
2. $6x-10y=3600⟹3x-5y=1800$

From equation (2), solve for $x$:

$$3x=1800+5y⟹x=\frac{1800+5y}{3}$$

Substitute this value of $x$ into equation (1):

$$5\left(\frac{1800+5y}{3}\right)-9y=2600$$

$$\frac{9000+25y}{3}-9y=2600$$

$$9000+25y-27y=7800$$

$$9000-2y=7800$$

$$2y=1200⟹y=600$$

Now find $x$:

$$x=\frac{1800+5(600)}{3}=\frac{1800+3000}{3}=\frac{4800}{3}=1600$$

Now, calculate their incomes:

* First person's income = $10x=10\times 1600=₹16,000$
* Second person's income = $6x=6\times 1600=₹9,600$