If 20% of the girls enrolled in science change their stream to Management, then what will be the new number of Management students altogether?

Number of students enrolled in various streams:
$$\eqalign{ & \text{IT → } \frac{20}{100}\times3500 = 700 \cr & \text{Arts → } \frac{30}{100}\times3500 = 1050 \cr & \text{Science → } \frac{22}{100}\times3500 = 770 \cr & \text{Commerce → } \frac{12}{100}\times3500 = 420 \cr & \text{Management → } \frac{16}{100}\times3500 = 560 \cr} $$

Number of girls enrolled in various streams:
$$\eqalign{ & \text{IT → } \frac{18}{100}\times1500 = 270 \cr & \text{Arts → } \frac{38}{100}\times1500 = 570 \cr & \text{Science → } \frac{11}{100}\times1500 = 165 \cr & \text{Commerce → } \frac{21}{100}\times1500 = 315 \cr & \text{Management → } \frac{12}{100}\times1500 = 180 \cr} $$

Number of Management students already enrolled = 560
New required number
$$\eqalign{ & = 560 + \left(\frac{20}{100}\times165\right) \cr & = 560+33 \cr & = 593 \cr} $$