A tailor sold a suit and a shirt for GH¢14,800, making a 20% profit on the suit and a 10% profit on the shirt. If he had sold the suit for a 10% profit and the shirt for a 20% profit, he would have re

Let $C_S$ be the cost price of the suit.
Let $C_H$ be the cost price of the shirt.

In the first scenario, the total selling price is GH¢14,800.
The profit on the suit is 20%, so its selling price is $C_S + 0.20 C_S = 1.20 C_S$.
The profit on the shirt is 10%, so its selling price is $C_H + 0.10 C_H = 1.10 C_H$.
This gives us the first equation:

In the second scenario, the total selling price is GH¢15,100.
If the profit on the suit were 10%, its selling price would be $C_S + 0.10 C_S = 1.10 C_S$.
If the profit on the shirt were 20%, its selling price would be $C_H + 0.20 C_H = 1.20 C_H$.
This gives us the second equation:

We have the system:

1. $1.2 C_S + 1.1 C_H = 14800$
2. $1.1 C_S + 1.2 C_H = 15100$

Multiply equation (1) by 1.2 and equation (2) by 1.1 to eliminate $C_H$:
$1.2 \times (1.2 C_S + 1.1 C_H) = 1.2 \times 14800 \implies 1.44 C_S + 1.32 C_H = 17760 \quad (3)$
$1.1 \times (1.1 C_S + 1.2 C_H) = 1.1 \times 15100 \implies 1.21 C_S + 1.32 C_H = 16610 \quad (4)$

Subtract equation (4) from equation (3):
$(1.44 C_S + 1.32 C_H) - (1.21 C_S + 1.32 C_H) = 17760 - 16610$
$0.23 C_S = 1150$

Using equation (1):
$1.2(5000) + 1.1 C_H = 14800$
$6000 + 1.1 C_H = 14800$
$1.1 C_H = 14800 - 6000$
$1.1 C_H = 8800$

The cost price of the suit is GH¢5000.
The cost price of the shirt is GH¢8000.

The cost price of the suit is $\boxed{\text{GH¢}5000}$.
The cost price of the shirt is $\boxed{\text{GH¢}8000}$.