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In a certain country, all the people are fans of exactly one of the following clubs, Real Madrid, Barcelona and Juventus. The percentage of people who follow Real Madrid is 60%. Out of these, 80% are followers of Cristiano. In the transfer season, Cristiano moved to Juventus. As a result, 50% of the Real Madrid followers who followed Cristiano stopped following Real Madrid and started following Juventus. Also, 25% of the Real Madrid followers who did not follow Cristiano stopped following Real Madrid and started following Barcelona. If the absolute difference between the final number of Juventus and Barcelona fans is equal to the final number of Real Madrid fans, what percentage of the population of the country initially followed Barcelona?
- a)14
- b)24
- c)40
- d)16
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a certain country, all the people are fans of exactly one of the fo...
Let the number of people in the country be 100.
Hence, the number of people following Real Madrid = 60
Let the number of people who follow Barcelona be x.
Hence, the number of people who follow Juventus = 40 - x.
The number of people following Cristiano among the Real Madrid followers = 0.8 x 60 = 48
The number of people not following Cristiano among the Real Madrid followers = 60 - 48 = 12.
The number of people who stopped following Real Madrid and started following Juventus = 0.5 x 48 = 24.
The number of people who stopped following Real Madrid and started following Barcelona = 0.25 x 12 = 3.
Number of people who still follow Real Madrid = (48 - 24) + (12 - 3) = 24 + 9 = 33.
Number of people who now follow Barcelona = x + 3
Number of people who now follow Juventus = 40 - x + 24 = 64 - x
Hence,
Case 1: x + 3 - 64 + x = 33
2x = 94
x = 47. (Not possible because 40 - x would become -7)
Case 2: 64 - x - x - 3 = 33
2x = 28
x = 14
Hence, the number of people following Real Madrid = 60
Let the number of people who follow Barcelona be x.
Hence, the number of people who follow Juventus = 40 - x.
The number of people following Cristiano among the Real Madrid followers = 0.8 x 60 = 48
The number of people not following Cristiano among the Real Madrid followers = 60 - 48 = 12.
The number of people who stopped following Real Madrid and started following Juventus = 0.5 x 48 = 24.
The number of people who stopped following Real Madrid and started following Barcelona = 0.25 x 12 = 3.
Number of people who still follow Real Madrid = (48 - 24) + (12 - 3) = 24 + 9 = 33.
Number of people who now follow Barcelona = x + 3
Number of people who now follow Juventus = 40 - x + 24 = 64 - x
Hence,
Case 1: x + 3 - 64 + x = 33
2x = 94
x = 47. (Not possible because 40 - x would become -7)
Case 2: 64 - x - x - 3 = 33
2x = 28
x = 14
Most Upvoted Answer
In a certain country, all the people are fans of exactly one of the fo...
To solve this question, let's break it down step by step:
1. Total Percentage of Real Madrid Followers:
- Given that 60% of the population follows Real Madrid.
2. Percentage of Real Madrid Followers Who Follow Cristiano:
- Given that 80% of Real Madrid followers follow Cristiano.
- Therefore, the percentage of Real Madrid followers who follow Cristiano is 60% * 80% = 48%.
3. Percentage of Real Madrid Followers Who Don't Follow Cristiano:
- Subtracting the percentage of Real Madrid followers who follow Cristiano from the total percentage of Real Madrid followers, we get 60% - 48% = 12%.
4. Changes After Cristiano Moved to Juventus:
- 50% of the Real Madrid followers who followed Cristiano started following Juventus.
- 25% of the Real Madrid followers who did not follow Cristiano started following Barcelona.
5. Final Number of Juventus Fans:
- Since 50% of the Real Madrid followers who followed Cristiano started following Juventus, the percentage of Juventus fans after the transfer would be 48% + 50% = 98%.
6. Final Number of Barcelona Fans:
- Since 25% of the Real Madrid followers who did not follow Cristiano started following Barcelona, the percentage of Barcelona fans after the transfer would be 12% + 25% = 37%.
7. Final Number of Real Madrid Fans:
- To find the final number of Real Madrid fans, we need to subtract the fans who switched to other clubs from the initial 60%.
- Since 50% of the Real Madrid followers who followed Cristiano switched to Juventus and 25% of the Real Madrid followers who did not follow Cristiano switched to Barcelona, the final percentage of Real Madrid fans would be 60% - 50% - 25% = 35%.
8. Absolute Difference between Juventus and Barcelona Fans:
- The absolute difference between the final number of Juventus and Barcelona fans is 98% - 37% = 61%.
9. Percentage of Population Initially Following Barcelona:
- Since the absolute difference between the final number of Juventus and Barcelona fans is equal to the final number of Real Madrid fans, the percentage of the population initially following Barcelona would be 35% - 61% = -26%.
However, since the percentage of followers cannot be negative, we disregard this result.
10. Conclusion:
- Therefore, it is not possible to determine the percentage of the population initially following Barcelona based on the given information.
1. Total Percentage of Real Madrid Followers:
- Given that 60% of the population follows Real Madrid.
2. Percentage of Real Madrid Followers Who Follow Cristiano:
- Given that 80% of Real Madrid followers follow Cristiano.
- Therefore, the percentage of Real Madrid followers who follow Cristiano is 60% * 80% = 48%.
3. Percentage of Real Madrid Followers Who Don't Follow Cristiano:
- Subtracting the percentage of Real Madrid followers who follow Cristiano from the total percentage of Real Madrid followers, we get 60% - 48% = 12%.
4. Changes After Cristiano Moved to Juventus:
- 50% of the Real Madrid followers who followed Cristiano started following Juventus.
- 25% of the Real Madrid followers who did not follow Cristiano started following Barcelona.
5. Final Number of Juventus Fans:
- Since 50% of the Real Madrid followers who followed Cristiano started following Juventus, the percentage of Juventus fans after the transfer would be 48% + 50% = 98%.
6. Final Number of Barcelona Fans:
- Since 25% of the Real Madrid followers who did not follow Cristiano started following Barcelona, the percentage of Barcelona fans after the transfer would be 12% + 25% = 37%.
7. Final Number of Real Madrid Fans:
- To find the final number of Real Madrid fans, we need to subtract the fans who switched to other clubs from the initial 60%.
- Since 50% of the Real Madrid followers who followed Cristiano switched to Juventus and 25% of the Real Madrid followers who did not follow Cristiano switched to Barcelona, the final percentage of Real Madrid fans would be 60% - 50% - 25% = 35%.
8. Absolute Difference between Juventus and Barcelona Fans:
- The absolute difference between the final number of Juventus and Barcelona fans is 98% - 37% = 61%.
9. Percentage of Population Initially Following Barcelona:
- Since the absolute difference between the final number of Juventus and Barcelona fans is equal to the final number of Real Madrid fans, the percentage of the population initially following Barcelona would be 35% - 61% = -26%.
However, since the percentage of followers cannot be negative, we disregard this result.
10. Conclusion:
- Therefore, it is not possible to determine the percentage of the population initially following Barcelona based on the given information.
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In a certain country, all the people are fans of exactly one of the following clubs, Real Madrid, Barcelona and Juventus. The percentage of people who follow Real Madrid is 60%. Out of these, 80% are followers of Cristiano. In the transfer season, Cristiano moved to Juventus. As a result, 50% of the Real Madrid followers who followed Cristiano stopped following Real Madrid and started following Juventus. Also, 25% of the Real Madrid followers who did not follow Cristiano stopped following Real Madrid and started following Barcelona. If the absolute difference between the final number of Juventus and Barcelona fans is equal to the final number of Real Madrid fans, what percentage of the population of the country initially followed Barcelona?a)14b)24c)40d)16Correct answer is option 'A'. Can you explain this answer?
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