The proportion of the number of students in three classes is 1 : 2 : 3. If 20 students are included in each class, then the proportion becomes 3 : 5 : 7. What was initially the total number of students in the three classes?

The proportion of the number of students in three classes is 1 : 2 : 3.

Let's assume the number of students in three classes is y, 2y, and 3y respectively.

If 20 students are included in each class, then the proportion becomes 3 : 5 : 7.

(y+20) : (2y+20) : (3y+20) :: 3 : 5 : 7

$$\frac{(y+20)}{(2y+20)}\ =\ \frac{3}{5}$$

$$5y+100=\ 6y+60$$

6y-5y = 100-60

y = 40

initially the total number of students in the three classes = y+2y+3y = 6y

= $$6\times40$$

= 240