CEMC Fermat

Since there are 30 people in a room and 60% of them are men, then there are $\frac{6}{10} \times 30=18$ men in the room and 12 women. Since no men enter or leave the room, then these 18 men represent 40% of the final number in the room. Thus, 9 men represent 20% of the the final number in the room, and so the final number of people is $5 \times 9=45$. Since 18 of these are men and 12 of these are the women originally in the room, then $45-18-12=15$ women entered the room.