Two skilled and three unskilled labourers cost sh. 3 500 per day. Three skilled and four unskilled labourers cost sh. 5 000 per day. Find the cost of hiring each skilled and unskilled labourer.

Let $s$ be the cost of hiring one skilled labourer per day.
Let $u$ be the cost of hiring one unskilled labourer per day.

From the problem statement, we can form two linear equations:
The cost for two skilled and three unskilled labourers is sh. 3 500:

$$2s + 3u = 3500 \quad (1)$$

The cost for three skilled and four unskilled labourers is sh. 5 000:

$$3s + 4u = 5000 \quad (2)$$

Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of $s$ equal:

$$3 \times (2s + 3u) = 3 \times 3500 \implies 6s + 9u = 10500 \quad (3)$$ $$2 \times (3s + 4u) = 2 \times 5000 \implies 6s + 8u = 10000 \quad (4)$$

$$(6s + 9u) - (6s + 8u) = 10500 - 10000$$ $$u = 500$$

$$2s + 3(500) = 3500$$ $$2s + 1500 = 3500$$ $$2s = 3500 - 1500$$ $$2s = 2000$$ $$s = 1000$$

The cost of hiring each skilled labourer is sh. 1000 per day, and the cost of hiring each unskilled labourer is sh. 500 per day.

The cost of hiring a skilled labourer is $\boxed{\text{sh. 1000}}$ per day.
The cost of hiring an unskilled labourer is $\boxed{\text{sh. 500}}$ per day.