Five day scholars and three boarders pay sh. 17000. Three day scholars and two boarders pay sh. 11000. Find the fees for each day scholar and each boarder.

Let $x$ be the school fees for one day scholar.
Let $y$ be the charge for one boarder per day.

From the problem statement, we can form two linear equations:
The total fees for five day scholars and three boarders is sh. 17000:

$$5x + 3y = 17000 \quad (1)$$

The total fees for three day scholars and two boarders is sh. 11000:

$$3x + 2y = 11000 \quad (2)$$

To eliminate $y$, multiply equation (1) by 2 and equation (2) by 3:

$$2 \times (5x + 3y) = 2 \times 17000 \implies 10x + 6y = 34000 \quad (3)$$ $$3 \times (3x + 2y) = 3 \times 11000 \implies 9x + 6y = 33000 \quad (4)$$

$$(10x + 6y) - (9x + 6y) = 34000 - 33000$$ $$x = 1000$$

$$3(1000) + 2y = 11000$$ $$3000 + 2y = 11000$$ $$2y = 11000 - 3000$$ $$2y = 8000$$ $$y = 4000$$

The school fees for each day scholar is sh. 1000.
The charge for each boarder is sh. 4000 per day.

The school fees for a day scholar is $\boxed{\text{sh. 1000}}$.
The charge for a boarder is $\boxed{\text{sh. 4000}}$ per day.