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In a class, some students play cricket and some play hockey. The students who play cricket is twice in number than those who play only hockey. The students who takes hockey are double in number than those who play only cricket. Consider the following statements and find correct ones:
Sum total of those students who play either cricket or hockey or both is thrice of those who play both cricket and hockey.
Sum total of those who play only cricket and only hockey, is twice the number of students playing both cricket and hockey.
- a)1 only
- b)2 only
- c)1 and 2 both
- d)None
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
In a class, some students play cricket and some play hockey. The stud...
Let number of students who play cricket =x
Let number of students who play hockey = y
Let number of students who play both cricket and hockey = C
Now as per information in questions:
x = 2 (y- C) …………(i)
y = 2 (x- C) ………….(ii)
Putting value of y from equation (ii) in equation (i)
x= 2 [2 (x- C)- C] = 2 [2x - 3C]
= 4x- 6C
or ax = 2C (iii)
Now, putting value in equation (ii)
y= 2c ... (iv)
Sum total of those students who play either cricket or hockey or both;
S, = (x - C)+ (y- C)+ C = (2C- C)+ (2C- C)+ C
= C + C = 3C
Some total of those who play only cricket and only hockey
S2 = - + (y- C)= (2C- C)+ (2C- C)= C + C = 2C
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Community Answer
In a class, some students play cricket and some play hockey. The stud...
The given problem can be solved using a Venn diagram representation:
Let's assume there are 'x' students who play cricket and 'y' students who play hockey.
Statement 1: The students who play cricket are twice in number than those who play only hockey.
This statement can be represented as:
Cricket players = 2 * (Hockey players)
Statement 2: The students who play hockey are double in number than those who play only cricket.
This statement can be represented as:
Hockey players = 2 * (Cricket players)
Statement 3: The sum total of those students who play either cricket or hockey or both is thrice of those who play both cricket and hockey.
Let's assume there are 'a' students who play both cricket and hockey.
The sum total of those who play either cricket or hockey or both is:
(Cricket players) + (Hockey players) - (Both cricket and hockey players)
= x + y - a
The number of students who play both cricket and hockey is:
a
According to the statement, the sum total is thrice the number of students who play both cricket and hockey:
x + y - a = 3a
Statement 4: The sum total of those who play only cricket and only hockey is twice the number of students playing both cricket and hockey.
The sum total of those who play only cricket is:
(Cricket players) - (Both cricket and hockey players)
= x - a
The sum total of those who play only hockey is:
(Hockey players) - (Both cricket and hockey players)
= y - a
The sum total of those who play only cricket and only hockey is:
(x - a) + (y - a) = x + y - 2a
According to the statement, the sum total is twice the number of students who play both cricket and hockey:
x + y - 2a = 2a
Solving the equations:
From Statement 2, we have:
Hockey players = 2 * (Cricket players)
y = 2x
Substituting this value in Statement 1, we get:
Cricket players = 2 * (Hockey players)
x = 2y
Solving these two equations, we find:
x = 4, y = 2
Substituting these values in Statement 3, we get:
x + y - a = 3a
4 + 2 - a = 3a
6 - a = 3a
4a = 6
a = 1
Substituting these values in Statement 4, we get:
x + y - 2a = 2a
4 + 2 - 2 = 2
4 = 2
Conclusion:
From the above calculations, we can conclude that the correct statements are:
1) The sum total of those students who play either cricket or hockey or both is thrice of those who play both cricket and hockey.
2) The sum total of those who play only cricket and only hockey is twice the number of students playing both cricket and hockey.
Let's assume there are 'x' students who play cricket and 'y' students who play hockey.
Statement 1: The students who play cricket are twice in number than those who play only hockey.
This statement can be represented as:
Cricket players = 2 * (Hockey players)
Statement 2: The students who play hockey are double in number than those who play only cricket.
This statement can be represented as:
Hockey players = 2 * (Cricket players)
Statement 3: The sum total of those students who play either cricket or hockey or both is thrice of those who play both cricket and hockey.
Let's assume there are 'a' students who play both cricket and hockey.
The sum total of those who play either cricket or hockey or both is:
(Cricket players) + (Hockey players) - (Both cricket and hockey players)
= x + y - a
The number of students who play both cricket and hockey is:
a
According to the statement, the sum total is thrice the number of students who play both cricket and hockey:
x + y - a = 3a
Statement 4: The sum total of those who play only cricket and only hockey is twice the number of students playing both cricket and hockey.
The sum total of those who play only cricket is:
(Cricket players) - (Both cricket and hockey players)
= x - a
The sum total of those who play only hockey is:
(Hockey players) - (Both cricket and hockey players)
= y - a
The sum total of those who play only cricket and only hockey is:
(x - a) + (y - a) = x + y - 2a
According to the statement, the sum total is twice the number of students who play both cricket and hockey:
x + y - 2a = 2a
Solving the equations:
From Statement 2, we have:
Hockey players = 2 * (Cricket players)
y = 2x
Substituting this value in Statement 1, we get:
Cricket players = 2 * (Hockey players)
x = 2y
Solving these two equations, we find:
x = 4, y = 2
Substituting these values in Statement 3, we get:
x + y - a = 3a
4 + 2 - a = 3a
6 - a = 3a
4a = 6
a = 1
Substituting these values in Statement 4, we get:
x + y - 2a = 2a
4 + 2 - 2 = 2
4 = 2
Conclusion:
From the above calculations, we can conclude that the correct statements are:
1) The sum total of those students who play either cricket or hockey or both is thrice of those who play both cricket and hockey.
2) The sum total of those who play only cricket and only hockey is twice the number of students playing both cricket and hockey.
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In a class, some students play cricket and some play hockey. The students who play cricket is twice in number than those who play only hockey. The students who takes hockey are double in number than those who play only cricket. Consider the following statements and find correct ones: Sum total of those students who play either cricket or hockey or both is thrice of those who play both cricket and hockey. Sum total of those who play only cricket and only hockey, is twice the number of students playing both cricket and hockey. a)1 onlyb)2 onlyc)1 and 2 bothd)NoneCorrect answer is option 'C'. Can you explain this answer?
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In a class, some students play cricket and some play hockey. The students who play cricket is twice in number than those who play only hockey. The students who takes hockey are double in number than those who play only cricket. Consider the following statements and find correct ones: Sum total of those students who play either cricket or hockey or both is thrice of those who play both cricket and hockey. Sum total of those who play only cricket and only hockey, is twice the number of students playing both cricket and hockey. a)1 onlyb)2 onlyc)1 and 2 bothd)NoneCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In a class, some students play cricket and some play hockey. The students who play cricket is twice in number than those who play only hockey. The students who takes hockey are double in number than those who play only cricket. Consider the following statements and find correct ones: Sum total of those students who play either cricket or hockey or both is thrice of those who play both cricket and hockey. Sum total of those who play only cricket and only hockey, is twice the number of students playing both cricket and hockey. a)1 onlyb)2 onlyc)1 and 2 bothd)NoneCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class, some students play cricket and some play hockey. The students who play cricket is twice in number than those who play only hockey. The students who takes hockey are double in number than those who play only cricket. Consider the following statements and find correct ones: Sum total of those students who play either cricket or hockey or both is thrice of those who play both cricket and hockey. Sum total of those who play only cricket and only hockey, is twice the number of students playing both cricket and hockey. a)1 onlyb)2 onlyc)1 and 2 bothd)NoneCorrect answer is option 'C'. Can you explain this answer?.
In a class, some students play cricket and some play hockey. The students who play cricket is twice in number than those who play only hockey. The students who takes hockey are double in number than those who play only cricket. Consider the following statements and find correct ones: Sum total of those students who play either cricket or hockey or both is thrice of those who play both cricket and hockey. Sum total of those who play only cricket and only hockey, is twice the number of students playing both cricket and hockey. a)1 onlyb)2 onlyc)1 and 2 bothd)NoneCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about In a class, some students play cricket and some play hockey. The students who play cricket is twice in number than those who play only hockey. The students who takes hockey are double in number than those who play only cricket. Consider the following statements and find correct ones: Sum total of those students who play either cricket or hockey or both is thrice of those who play both cricket and hockey. Sum total of those who play only cricket and only hockey, is twice the number of students playing both cricket and hockey. a)1 onlyb)2 onlyc)1 and 2 bothd)NoneCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class, some students play cricket and some play hockey. The students who play cricket is twice in number than those who play only hockey. The students who takes hockey are double in number than those who play only cricket. Consider the following statements and find correct ones: Sum total of those students who play either cricket or hockey or both is thrice of those who play both cricket and hockey. Sum total of those who play only cricket and only hockey, is twice the number of students playing both cricket and hockey. a)1 onlyb)2 onlyc)1 and 2 bothd)NoneCorrect answer is option 'C'. Can you explain this answer?.
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