Of $450$ students assembled for a concert, $40$ percent were boys. After a bus containing an equal number of boys and girls brought more students to the concert, $41$ percent of the students at the concert were boys. Find the number of students on the bus.
1. Initially, there are 450 students at the concert, and 40% of them are boys. We can calculate the number of boys and girls initially as follows:
   \[
   \text{Number of boys} = 0.40 \times 450 = 180
   \]
   \[
   \text{Number of girls} = 450 - 180 = 270
   \]

2. Let \(2x\) be the number of students on the bus, where \(x\) is the number of boys and \(x\) is the number of girls (since the bus contains an equal number of boys and girls).

3. After the bus arrives, the total number of students at the concert becomes:
   \[
   450 + 2x
   \]
   The total number of boys becomes:
   \[
   180 + x
   \]

4. According to the problem, after the bus arrives, 41% of the students at the concert are boys. Therefore, we can set up the following equation:
   \[
   \frac{180 + x}{450 + 2x} = 0.41
   \]

5. To solve for \(x\), we first clear the fraction by multiplying both sides by \(450 + 2x\):
   \[
   180 + x = 0.41 \times (450 + 2x)
   \]

6. Distribute 0.41 on the right-hand side:
   \[
   180 + x = 0.41 \times 450 + 0.41 \times 2x
   \]
   \[
   180 + x = 184.5 + 0.82x
   \]

7. Isolate \(x\) by moving all terms involving \(x\) to one side and constants to the other side:
   \[
   180 + x - 0.82x = 184.5
   \]
   \[
   180 + 0.18x = 184.5
   \]

8. Subtract 180 from both sides:
   \[
   0.18x = 4.5
   \]

9. Solve for \(x\) by dividing both sides by 0.18:
   \[
   x = \frac{4.5}{0.18} = 25
   \]

10. Since \(2x\) is the total number of students on the bus, we have:
    \[
    2x = 2 \times 25 = 50
    \]

The final answer is \(\boxed{50}\).