Question

At a football match, A third of the spectators were boys, while a quarter were girls. Three fifths of the remainder were men and the rest were women. What fraction of the total attendance were women? A. 1/6 B. 7/12 C. 1/4 D. 5/12

Answer 1

Answer:

Option A = 1/6

Step-by-step explanation:

[First of all, thanks for the question. It was really fun to solve :) ]

Let the total number of spectators be x.

Given, one third of them were boys and one quarter of them were girls. So that means:

Number of boys = $\frac{x}{3}$

Number of girls = $\frac{x}{4}$

So the remaining fraction of people left:

$x - (\frac{x}{3} + \frac{x}{4}) = x - \frac{7x}{12} = \frac{5x}{12}$

Now given that, out of the remaining people, three-fifths were men. That means, two-fifths of the remaining are, yes you're right, women. So,

Number of women = $\frac{2}{5} * \frac{5x}{12} = \frac{x}{6}$

Since in question, they gave the fraction of attendees, You can make x = 1.

That gives your fraction as = $\frac{1}{6}$.

I hope this helps :)

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