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In a seminar the number of participants in Technology, Economics and Science are 150, 90 and 180 respectively. Find the minimum number of rooms required, where in each room the same number of participants are to be seated and all of them being in the same subject.
- a)27
- b)32
- c)30
- d)14
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In a seminar the number of participants in Technology, Economics and S...
HCF of 150, 90 and 180 = 30
No of participants can be seated in each room = 30
No of participants can be seated in each room = 30
There are total 420 participants.
As the HCF is 30 i.e. mininum number of participants in each room.
so total rooms required will be 420/30 = 14
Most Upvoted Answer
In a seminar the number of participants in Technology, Economics and S...
HCF of 150, 90 and 180 = 30
No of participants can be seated in each room = 30
No of participants can be seated in each room = 30
There are total 420 participants.
As the HCF is 30 i.e. mininum number of participants in each room.
so total rooms required will be 420/30 = 14
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Community Answer
In a seminar the number of participants in Technology, Economics and S...
To find the minimum number of rooms required, we need to determine the maximum number of participants that can be seated in each room.
Given:
Number of participants in Technology = 150
Number of participants in Economics = 90
Number of participants in Science = 180
We need to find the common factor (or divisor) of these numbers that will give us the maximum number of participants that can be seated in each room.
Finding Common Factor:
To find the common factor, we can list down the factors of each number and find the common factors among them.
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
From the above factor lists, we can see that the common factors among all three numbers are 1, 2, 3, 5, 6, 10, 15, 30.
Calculating Minimum Number of Rooms:
Now, we need to choose the largest common factor to determine the maximum number of participants that can be seated in each room.
The largest common factor is 30. Therefore, each room can accommodate a maximum of 30 participants.
To calculate the minimum number of rooms required, we divide the total number of participants in each subject by the maximum number of participants per room.
Number of rooms required for Technology = 150/30 = 5
Number of rooms required for Economics = 90/30 = 3
Number of rooms required for Science = 180/30 = 6
The total number of rooms required = 5 + 3 + 6 = 14
Therefore, the minimum number of rooms required is 14.
Hence, the correct answer is option D) 14.
Given:
Number of participants in Technology = 150
Number of participants in Economics = 90
Number of participants in Science = 180
We need to find the common factor (or divisor) of these numbers that will give us the maximum number of participants that can be seated in each room.
Finding Common Factor:
To find the common factor, we can list down the factors of each number and find the common factors among them.
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
From the above factor lists, we can see that the common factors among all three numbers are 1, 2, 3, 5, 6, 10, 15, 30.
Calculating Minimum Number of Rooms:
Now, we need to choose the largest common factor to determine the maximum number of participants that can be seated in each room.
The largest common factor is 30. Therefore, each room can accommodate a maximum of 30 participants.
To calculate the minimum number of rooms required, we divide the total number of participants in each subject by the maximum number of participants per room.
Number of rooms required for Technology = 150/30 = 5
Number of rooms required for Economics = 90/30 = 3
Number of rooms required for Science = 180/30 = 6
The total number of rooms required = 5 + 3 + 6 = 14
Therefore, the minimum number of rooms required is 14.
Hence, the correct answer is option D) 14.
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In a seminar the number of participants in Technology, Economics and Science are 150, 90 and 180 respectively. Find the minimum number of rooms required, where in each room the same number of participants are to be seated and all of them being in the same subject.a)27b)32c)30d)14e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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