The incomes of $A$ and $B$ are in the ratio $3:2$ and their expenditures are in the ratio $5:3$. If each individual manages to save $\text{Rs. }1,000$, then $B$ 's income is:

Let the incomes of $A$ and $B$ be $3x$ and $2x$ respectively. Let their expenditures be $5y$ and $3y$ respectively.
We know that:

$$\text{Income}-\text{Expenditure}=\text{Savings}$$

From the given conditions:

$$3x-5y=1000\text{— (Equation 1)}$$

$$2x-3y=1000\text{— (Equation 2)}$$

Let's equate the two expressions since both are equal to $1000$:

$$3x-5y=2x-3y$$

$$3x-2x=5y-3y⟹x=2y$$

Substitute $x=2y$ into Equation 2:

$$2(2y)-3y=1000$$

$$4y-3y=1000⟹y=1000$$

Now find the value of $x$:

$$x=2\times 1000=2000$$

The income of $B$ is defined as $2x$:

$$\text{Income of }B=2\times 2000=\text{Rs. }4,000$$