Percentages

[Abdulla]

A room contains 160 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?

(A) 10
(B) 20
(C) 40
(D) 60
(E) 80

OA is C

[cramya]

15% of 160 is women = 24

Let x represent people who left the room(30% of these are women + 10% of 160-x are women and these both must add up to the original number of women we found above i.e. 24)

.30x + .10(160-x) = 24

x=40

C)

[Abdulla]

always your approach is better than the Official Explantion..

Thanks

[canuckclint]

Found a good way to solve this algebraically.

Let x be people who left the room, y of which are women.
y/x = 30/100 --30% who left the room are women
(24-y)/(160-x) = 10/100 --people left in the room 10% are women

2400 - 100y = 1600 - 10x
800 = 100y - 10x
800 = 100(x*30/100) - 10x
800 = 20x
x = 40