Question

There were only men and women in a hall. The number of men was 624 more than the number of women. When one-third of the men and 436 of the women left the hall, three-fifths of the people left in the hall were men. How many women were there in the hall at first?

a) 780 women
b) 936 women
c) 1248 women
d) 1560 women

Answer 1

To solve the problem, the number of women in the hall can be represented by 'w'. After one-third of the men and 436 of the women left, the number of men remaining is (2/3)(w + 624) and the number of women remaining is (w - 436). Setting up an equation and solving for 'w' gives the answer of 780 women in the hall at first.

Step-by-step explanation:

To solve this problem, let's use algebraic expressions. Let the number of women in the hall be represented by 'w'. The number of men would then be 'w + 624'.

After one-third of the men and 436 of the women left, the number of men remaining would be (2/3)(w + 624) and the number of women remaining would be (w - 436).

According to the given information, (3/5) of the remaining people in the hall were men. So we can write the following equation:

(2/3)(w + 624) = (3/5)[(2/3)(w + 624) + (w - 436)]

Simplifying and solving for 'w', we get:

w = 780

Therefore, there were 780 women in the hall at first.