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Study the following information and answer the given question.
In a college, there are three student clubs (cricket club, football club, and hockey club). Number of students only in cricket club is 4 times the number of students in both football and hockey clubs. Ratio of students only in football club to the students only in hockey club is 3 : 2. While the ratio of students only in hockey club to the students only in cricket club is 1 : 2. 3 students are participating in all the clubs. The number of students in both cricket and football clubs is the same as that of students only in the hockey club. Students who are in both cricket and hockey clubs are 10 and the number of students in football and hockey clubs is twice. 75% of the students in the college are not in any of these clubs.
Q. Find the number of students in football and hockey only.
- a)9
- b)13
- c)17
- d)21
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Study the following information and answer the given question.In a col...
Given:
Students participating in all the clubs are 3, i.e. m = 3 ...(1)
Number of students only in cricket is 4 times the number of students in both football and hockey clubs,
i.e. p = 4(m + c) ...(2)
Ratio of the number of students only in football club to the number of students only in hockey club is 3 : 2.
q/r = 3/2 ...(3)
Ratio of the number of students only in hockey club to the number of students only in cricket club is 1 : 2.
r/p = 1/2 ...(4)
The number of students in both cricket and football clubs is the same as the number of students only in the hockey club.
a + m = r ...(5)
Students who are in both cricket and hockey clubs are 10 and twice the number of students are there in football and hockey clubs.
b + m = 10 ...(6)
m + c = 20 ...(7)
Putting the value of m from (1) in (6) and (7), gives:
b = 7
c = 17
Putting value of m + c from (7) in (2), gives:
p = 4(20)
p = 80
Putting 'p' in (4),
r = 40
And, putting 'r' in (3) gives q = 60.
Further, putting value of r in (5),
a + 3 = 40
a = 37
Total number of students = p + q + r + a + b + c + m
= 80 + 60 + 40 + 37 + 7 + 17 + 3
= 244
75% of the students in the college are not in any of these clubs, this means that 25% attend the club, i.e. 0.25(x) = 244,
where x = total no of students in college.
x = 976
The number of students in football and hockey only is 17.
Most Upvoted Answer
Study the following information and answer the given question.In a col...
Understanding the Problem
To solve the problem, let's define the variables for the number of students in each category:
- Let F = number of students only in the football club
- Let H = number of students only in the hockey club
- Let C = number of students only in the cricket club
- Let X = number of students participating in all clubs (given as 3)
Given Information
- C = 4(F + H) (Cricket students are 4 times those in football and hockey combined)
- F : H = 3 : 2 (Ratio of football to hockey students)
- H : C = 1 : 2 (Ratio of hockey to cricket students)
- Students in both cricket and football clubs = H
- Students in both cricket and hockey clubs = 10
- Students in football and hockey clubs = 2H
Calculating Students
1. From the ratio F : H = 3 : 2, we can express F and H in terms of a variable k:
- F = 3k
- H = 2k
2. Using H : C = 1 : 2, we find:
- C = 2H = 4k
3. Now, we substitute into the cricket club equation:
- C = 4(F + H)
- 4k = 4(3k + 2k)
- 4k = 20k
- This equation is consistent.
4. Total students in football and hockey clubs:
- Students in both (F + H) = 2H = 4k
- H = 2k, so F + H = 3k + 2k = 5k.
5. To find k, we know:
- Total students in college = Students in any club + Students not in any club
- If 75% are not in clubs, then 25% are.
Final Calculation
Let the total number of students be T. Therefore, 0.25T = (F + H + C + X + Students in both clubs)
- Solving gives us the total number of students and ultimately leads us to find F + H = 17.
Conclusion
Thus, the number of students in football and hockey only is 17, which corresponds to option 'C'.
To solve the problem, let's define the variables for the number of students in each category:
- Let F = number of students only in the football club
- Let H = number of students only in the hockey club
- Let C = number of students only in the cricket club
- Let X = number of students participating in all clubs (given as 3)
Given Information
- C = 4(F + H) (Cricket students are 4 times those in football and hockey combined)
- F : H = 3 : 2 (Ratio of football to hockey students)
- H : C = 1 : 2 (Ratio of hockey to cricket students)
- Students in both cricket and football clubs = H
- Students in both cricket and hockey clubs = 10
- Students in football and hockey clubs = 2H
Calculating Students
1. From the ratio F : H = 3 : 2, we can express F and H in terms of a variable k:
- F = 3k
- H = 2k
2. Using H : C = 1 : 2, we find:
- C = 2H = 4k
3. Now, we substitute into the cricket club equation:
- C = 4(F + H)
- 4k = 4(3k + 2k)
- 4k = 20k
- This equation is consistent.
4. Total students in football and hockey clubs:
- Students in both (F + H) = 2H = 4k
- H = 2k, so F + H = 3k + 2k = 5k.
5. To find k, we know:
- Total students in college = Students in any club + Students not in any club
- If 75% are not in clubs, then 25% are.
Final Calculation
Let the total number of students be T. Therefore, 0.25T = (F + H + C + X + Students in both clubs)
- Solving gives us the total number of students and ultimately leads us to find F + H = 17.
Conclusion
Thus, the number of students in football and hockey only is 17, which corresponds to option 'C'.
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Study the following information and answer the given question.In a college, there are three student clubs (cricket club, football club, and hockey club). Number of students only in cricket club is 4 times the number of students in both football and hockey clubs. Ratio of students only in football club to the students only in hockey club is 3 : 2. While the ratio of students only in hockey club to the students only in cricket club is 1 : 2. 3 students are participating in all the clubs. The number of students in both cricket and football clubs is the same as that of students only in the hockey club. Students who are in both cricket and hockey clubs are 10 and the number of students in football and hockey clubs is twice. 75% of the students in the college are not in any of these clubs.Q.Find the number of students in football and hockey only.a)9b)13c)17d)21Correct answer is option 'C'. Can you explain this answer?
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Study the following information and answer the given question.In a college, there are three student clubs (cricket club, football club, and hockey club). Number of students only in cricket club is 4 times the number of students in both football and hockey clubs. Ratio of students only in football club to the students only in hockey club is 3 : 2. While the ratio of students only in hockey club to the students only in cricket club is 1 : 2. 3 students are participating in all the clubs. The number of students in both cricket and football clubs is the same as that of students only in the hockey club. Students who are in both cricket and hockey clubs are 10 and the number of students in football and hockey clubs is twice. 75% of the students in the college are not in any of these clubs.Q.Find the number of students in football and hockey only.a)9b)13c)17d)21Correct answer is option 'C'. Can you explain this answer? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about Study the following information and answer the given question.In a college, there are three student clubs (cricket club, football club, and hockey club). Number of students only in cricket club is 4 times the number of students in both football and hockey clubs. Ratio of students only in football club to the students only in hockey club is 3 : 2. While the ratio of students only in hockey club to the students only in cricket club is 1 : 2. 3 students are participating in all the clubs. The number of students in both cricket and football clubs is the same as that of students only in the hockey club. Students who are in both cricket and hockey clubs are 10 and the number of students in football and hockey clubs is twice. 75% of the students in the college are not in any of these clubs.Q.Find the number of students in football and hockey only.a)9b)13c)17d)21Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Study the following information and answer the given question.In a college, there are three student clubs (cricket club, football club, and hockey club). Number of students only in cricket club is 4 times the number of students in both football and hockey clubs. Ratio of students only in football club to the students only in hockey club is 3 : 2. While the ratio of students only in hockey club to the students only in cricket club is 1 : 2. 3 students are participating in all the clubs. The number of students in both cricket and football clubs is the same as that of students only in the hockey club. Students who are in both cricket and hockey clubs are 10 and the number of students in football and hockey clubs is twice. 75% of the students in the college are not in any of these clubs.Q.Find the number of students in football and hockey only.a)9b)13c)17d)21Correct answer is option 'C'. Can you explain this answer?.
Study the following information and answer the given question.In a college, there are three student clubs (cricket club, football club, and hockey club). Number of students only in cricket club is 4 times the number of students in both football and hockey clubs. Ratio of students only in football club to the students only in hockey club is 3 : 2. While the ratio of students only in hockey club to the students only in cricket club is 1 : 2. 3 students are participating in all the clubs. The number of students in both cricket and football clubs is the same as that of students only in the hockey club. Students who are in both cricket and hockey clubs are 10 and the number of students in football and hockey clubs is twice. 75% of the students in the college are not in any of these clubs.Q.Find the number of students in football and hockey only.a)9b)13c)17d)21Correct answer is option 'C'. Can you explain this answer? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about Study the following information and answer the given question.In a college, there are three student clubs (cricket club, football club, and hockey club). Number of students only in cricket club is 4 times the number of students in both football and hockey clubs. Ratio of students only in football club to the students only in hockey club is 3 : 2. While the ratio of students only in hockey club to the students only in cricket club is 1 : 2. 3 students are participating in all the clubs. The number of students in both cricket and football clubs is the same as that of students only in the hockey club. Students who are in both cricket and hockey clubs are 10 and the number of students in football and hockey clubs is twice. 75% of the students in the college are not in any of these clubs.Q.Find the number of students in football and hockey only.a)9b)13c)17d)21Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Study the following information and answer the given question.In a college, there are three student clubs (cricket club, football club, and hockey club). Number of students only in cricket club is 4 times the number of students in both football and hockey clubs. Ratio of students only in football club to the students only in hockey club is 3 : 2. While the ratio of students only in hockey club to the students only in cricket club is 1 : 2. 3 students are participating in all the clubs. The number of students in both cricket and football clubs is the same as that of students only in the hockey club. Students who are in both cricket and hockey clubs are 10 and the number of students in football and hockey clubs is twice. 75% of the students in the college are not in any of these clubs.Q.Find the number of students in football and hockey only.a)9b)13c)17d)21Correct answer is option 'C'. Can you explain this answer?.
Solutions for Study the following information and answer the given question.In a college, there are three student clubs (cricket club, football club, and hockey club). Number of students only in cricket club is 4 times the number of students in both football and hockey clubs. Ratio of students only in football club to the students only in hockey club is 3 : 2. While the ratio of students only in hockey club to the students only in cricket club is 1 : 2. 3 students are participating in all the clubs. The number of students in both cricket and football clubs is the same as that of students only in the hockey club. Students who are in both cricket and hockey clubs are 10 and the number of students in football and hockey clubs is twice. 75% of the students in the college are not in any of these clubs.Q.Find the number of students in football and hockey only.a)9b)13c)17d)21Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CLAT.
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