In a school, 1200 of the students are boys. If 50% of the boys and 40% of the girls have paid their school fees, find the number of girls, given that 46% of the population has paid their school fees.

The total number of boys is 1200, and 50% of them have paid.

$$\text{Boys who paid} = 0.50 \times 1200 = 600$$

Let $G$ be the number of girls in the school.
The total population of students, $T$, is the sum of boys and girls.

$$T = 1200 + G$$

40% of the girls have paid their fees:

$$\text{Girls who paid} = 0.40 \times G$$

The total number of students who paid fees is 46% of the total population:

$$\text{Total paid} = 0.46 \times T = 0.46 \times (1200 + G)$$

The total number of students who paid fees is also the sum of boys who paid and girls who paid.

$$\text{Total paid} = \text{Boys who paid} + \text{Girls who paid}$$ $$0.46 \times (1200 + G) = 600 + 0.40G$$

Distribute 0.46 on the left side:

$$0.46 \times 1200 + 0.46G = 600 + 0.40G$$ $$552 + 0.46G = 600 + 0.40G$$

Subtract $0.40G$ from both sides:

$$552 + 0.46G - 0.40G = 600$$ $$552 + 0.06G = 600$$

Subtract 552 from both sides:

$$0.06G = 600 - 552$$ $$0.06G = 48$$

Divide by 0.06:

$$G = \frac{48}{0.06}$$ $$G = 800$$

The number of girls is 800.

The number of girls is $\text{800}$.