When a new group of 45 boys joined a concert, the ratio of the number of boys to the number of girls present became 2 : 3. The initial ratio was 5 : 9. How many more girls than boys were there in the end?

Step 1: Let's denote the initial number of boys as 5x and the initial number of girls as 9x (according to the initial ratio 5:9).

Step 2: After 45 boys joined, the number of boys became 5x + 45. The number of girls remained the same, 9x.

Step 3: According to the problem, after the boys joined, the ratio of boys to girls became 2:3. So, we can write the equation (5x + 45) / 9x = 2 / 3.

Step 4: Solve this equation to find the value of x. Cross multiply to get 3*(5x + 45) = 2*9x. Simplify to get 15x + 135 = 18x. Subtract 15x from both sides to get 135 = 3x. Divide both sides by 3 to get x = 45.

Step 5: Substitute x = 45 into the expressions for the number of boys and girls. The initial number of boys was 5x = 545 = 225 and the initial number of girls was 9x = 945 = 405.

Step 6: After 45 boys joined, the number of boys became 225 + 45 = 270. The number of girls remained the same, 405.

Step 7: To find out how many more girls than boys were there in the end, subtract the number of boys from the number of girls: 405 - 270 = 135.

So, there were 135 more girls than boys in the end.