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40% of the women are above 30 years of age and 80 percent of the women are less than or equal to 50 years of age. 20 percent of all women play basketball.If 30 percent of the women above the age of 50 plays basketball, what percent of players are less than or equal to 50 years?
- a)50%
- b)60%
- c)70%
- d)80%
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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40% of the women are above 30 years of age and 80 percent of the women...
Answer – c) 70% Explanation : take total women =100 Women less than or equal to 50 years = 80 and women above 50 years = 20 20 = women plays basketball 30% of the women above 50 plays basketball = 6 So remaining 14 women who plays basketball are less than or equal to 50 years So (14/20)*100 = 70%
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40% of the women are above 30 years of age and 80 percent of the women...
Given data:
- 40% of women are above 30 years of age
- 80% of women are less than or equal to 50 years of age
- 20% of all women play basketball
- 30% of women above the age of 50 play basketball
To find: What percent of players are less than or equal to 50 years?
Solution:
Let's assume there are 100 women in total. Then,
- 40 women are above 30 years of age (40% of 100)
- 80 women are less than or equal to 50 years of age (80% of 100)
- 20 women play basketball (20% of 100)
Now, out of the 40 women above 30 years of age, let's say x% play basketball. Then,
- Number of women above 30 years of age who play basketball = x% of 40 = 0.4x
Also, out of the 80 women less than or equal to 50 years of age, (100 - x)% play basketball. Then,
- Number of women less than or equal to 50 years of age who play basketball = (100 - x)% of 80 = 0.8(100 - x)
We are given that 30% of women above the age of 50 play basketball, which means 0.3 times the number of women above 50 years of age play basketball. So,
- Number of women above 50 years of age who play basketball = 0.3(40 - x)
The total number of women who play basketball is 20. Therefore,
- Number of women who play basketball = Number of women above 30 years of age who play basketball + Number of women less than or equal to 50 years of age who play basketball + Number of women above 50 years of age who play basketball
- 20 = 0.4x + 0.8(100 - x) + 0.3(40 - x)
- 20 = 0.4x + 80 - 0.8x + 12 - 0.3x
- 0.1x = -72
- x = 720/10 = 72
Therefore, out of the 40 women above 30 years of age, 72% play basketball. And out of the 80 women less than or equal to 50 years of age, (100 - 72)% = 28% play basketball.
Hence, the percentage of players who are less than or equal to 50 years of age = 20% - 72% + 28% = 76%.
Therefore, option C (70%) is incorrect. The correct answer is option E (None of these).
- 40% of women are above 30 years of age
- 80% of women are less than or equal to 50 years of age
- 20% of all women play basketball
- 30% of women above the age of 50 play basketball
To find: What percent of players are less than or equal to 50 years?
Solution:
Let's assume there are 100 women in total. Then,
- 40 women are above 30 years of age (40% of 100)
- 80 women are less than or equal to 50 years of age (80% of 100)
- 20 women play basketball (20% of 100)
Now, out of the 40 women above 30 years of age, let's say x% play basketball. Then,
- Number of women above 30 years of age who play basketball = x% of 40 = 0.4x
Also, out of the 80 women less than or equal to 50 years of age, (100 - x)% play basketball. Then,
- Number of women less than or equal to 50 years of age who play basketball = (100 - x)% of 80 = 0.8(100 - x)
We are given that 30% of women above the age of 50 play basketball, which means 0.3 times the number of women above 50 years of age play basketball. So,
- Number of women above 50 years of age who play basketball = 0.3(40 - x)
The total number of women who play basketball is 20. Therefore,
- Number of women who play basketball = Number of women above 30 years of age who play basketball + Number of women less than or equal to 50 years of age who play basketball + Number of women above 50 years of age who play basketball
- 20 = 0.4x + 0.8(100 - x) + 0.3(40 - x)
- 20 = 0.4x + 80 - 0.8x + 12 - 0.3x
- 0.1x = -72
- x = 720/10 = 72
Therefore, out of the 40 women above 30 years of age, 72% play basketball. And out of the 80 women less than or equal to 50 years of age, (100 - 72)% = 28% play basketball.
Hence, the percentage of players who are less than or equal to 50 years of age = 20% - 72% + 28% = 76%.
Therefore, option C (70%) is incorrect. The correct answer is option E (None of these).
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40% of the women are above 30 years of age and 80 percent of the women...
"40% of the women are above 30 years of age "
not used in question, this data should not be considered in solving or without this information it can be solved i.e this information is over sufficient
not used in question, this data should not be considered in solving or without this information it can be solved i.e this information is over sufficient
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40% of the women are above 30 years of age and 80 percent of the women are less than or equal to 50 years of age. 20 percent of all women play basketball.If 30 percent of the women above the age of 50 plays basketball, what percent of players are less than or equal to 50 years?a)50%b)60%c)70%d)80%e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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