A train fare for school children is half the fare of a teacher. The total fare for 120 children and 15 teachers for an excursion is GH¢180. i) Find the fare for a child. ii) How many children would go on the excursion with 20 teachers for a total fare of GH¢240.00?

Step 1: Define variables and set up equations based on the given information.
Let $C$ be the fare for a child and $T$ be the fare for a teacher.
From the problem, the fare for a school child is half the fare for a teacher:

$$C = \frac{1}{2}T \implies T = 2C$$

For the first excursion, 120 children and 15 teachers paid a total of GH¢180.
The total fare equation is:

$$120C + 15T = 180$$

Step 2: Solve for the fare of a child ($C$).
Substitute $T = 2C$ into the total fare equation:

$$120C + 15(2C) = 180$$ $$120C + 30C = 180$$ $$150C = 180$$ $$C = \frac{180}{150}$$ $$C = \frac{18}{15}$$ $$C = \frac{6}{5}$$ $$C = 1.20$$

The fare for a child is GH¢1.20.