In a school, there are 550 students. The ratio of the boys to that of the girls is 6 : 5. How many more girls should join the school so that the ratio becomes 5 : 6?

In a school, there are 550 students. The ratio of the boys to that of the girls is 6 : 5.

Let's assume initially the number of boys and girls are 6y and 5y respectively.

Total students initially = (6y+5y) = 550

11y = 550

y = 50

initially the number of boys = 6y = $$6\times50$$ = 300

initially the number of girls = 5y = $$5\times50$$ = 250

Let's assume the number of new girls to join the school is 'z'.

$$\frac{300}{250+z}\ =\ \frac{5}{6}$$

$$\frac{60}{250+z}\ =\ \frac{1}{6}$$

250+z = 360

z = 360-250 = 110