70% of stadium visitors are men. 1/7 of men and 1/5 of women at the st

Total no of visitors=10 x(say)
No of men=7x, no of women=3x
Male fans of visiting team=x
Female fans of visiting team=0.6 x
Male fans of home team=6x
Female fans of home team=2.4x
Therefore, 6x+2.4x=6300
x=750
Total no of visitors=7500
No of women=30% of 7500=2250
Answer C

Let T = Total number of fans in the stadium

Text in black: Given information
Text in red: Calculated values

To calculate T: 0.1 T + 0.06 T = 1200 ---> T = 7500.

Thus W = 0.3T = 2250. Thus C is the correct answer.

800score Official Solution:

Let's count the fraction of people supporting the visiting team.
70% of the stadium visitors are men, so 30% are women. We know what part of the men (1/7) and what part of women (1/5) support the visiting team, so we can find the fraction of the visiting team's fans out of the total:
(7/10) × (1/7) + (3/10) × (1/5) = 1/10 + 3/50 = 5/50 + 3/50 = 8/50 = 4/25.
If 4/25 of the fans support the visiting team, then 1 – 4/25 = 21/25 support the home team.
(21/25) × (people at the stadium) = 6300
(people at the stadium) = 6300 × 25/21 = 7500
Women are 30% of the visitors, 7500 × 30% = 2250.

The correct answer is choice (C).

The alternative explanation:
Instead of dealing with fractions, we can deal with percentages.

(C) Let's count the percentage of people supporting the visiting team.
70% of the stadium visitors are men, so 30% are women. We know what part of the men (1/7) and what part of women (1/5) support the visiting team, so we can find the percentage of the visiting team's fans out of the total:
70% × (1/7) + 30% × (1/5) = 10% + 6% = 16%.
If 16% of the fans support the visiting team, then 100% – 16% = 84% support the home team.
(84/100) × (people at the stadium) = 6300
(people at the stadium) = 6300 × 100 / 84 = 7500
30% are women: 7500 × 30 / 100 = 2250.

The correct answer is choice (C).

The alternative explanation #2:
You can consider 100% to be 100 persons.

Suppose there were 100 visitors, in which case there are 70 men and 30 women. 10 men support the visiting team and 60 men support the home team. Following through, 6 women support the visiting team and 24 women support the home team. This implies that 84% of the total number visiting the stadium are 6300 which sets up the equation:
(84/100) × P =6300,
where P is the actual total number visiting the stadium. Solving this equation gives P = (6300 x 100)/84 =7500 and 30% of this value is the number of women in the stadium which works out to 2250.

It normally takes me 3-4mins to solve 700+ correctly. Do you have any suggestion to reduce the time to about 2mins, Bunuel? I am sorry if my question is irrelevant here.

Given, men = 70 and Women =30, if Total persons =100
Fan for visiting team = 10 (from men) + 6 (from women) = 16

Fan for Home team = 60 (remaining men from visiting team) + 24 (remaining women from visiting team)= 84 = 6300 (given)

So, Total nos. of visitors = 6300/84 *100 = 7500
Nos. of women = 7500 * 30/100 = 2250.

So, I think C.

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