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In a classroom there are certain number of benches. If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench, then, after accommodating all of them, space for 5 students is left. What is the total number of students in the class?
- a)30
- b)42
- c)72
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Given:
- If 6 students are made to sit on a bench then one more bench is needed
- If 7 students are made to sit on a bench then space for 5 students is left
To find: Total number of students in the class
Let the total number of benches be x and the total number of students be y
From the first statement, we can write:
- 6 students can sit on 1 bench
- Therefore, x+1 benches are needed to accommodate y students
From the second statement, we can write:
- 7 students can sit on 1 bench and space for 5 students is left
- Therefore, x benches can accommodate y-5 students
Equating the above two expressions, we get:
x+1 = x + (y-5)/7
Simplifying the above expression, we get:
y = 12x + 30
We know that y and x are both positive integers. Therefore, we need to find a value of x such that y is also a positive integer.
Let's try some values of x:
- If x = 1, then y = 42
- If x = 2, then y = 54
- If x = 3, then y = 66
- If x = 4, then y = 78
The only value of x that gives a positive integer value of y is x = 6, which gives y = 72.
Therefore, the total number of students in the class is 72.
- If 6 students are made to sit on a bench then one more bench is needed
- If 7 students are made to sit on a bench then space for 5 students is left
To find: Total number of students in the class
Let the total number of benches be x and the total number of students be y
From the first statement, we can write:
- 6 students can sit on 1 bench
- Therefore, x+1 benches are needed to accommodate y students
From the second statement, we can write:
- 7 students can sit on 1 bench and space for 5 students is left
- Therefore, x benches can accommodate y-5 students
Equating the above two expressions, we get:
x+1 = x + (y-5)/7
Simplifying the above expression, we get:
y = 12x + 30
We know that y and x are both positive integers. Therefore, we need to find a value of x such that y is also a positive integer.
Let's try some values of x:
- If x = 1, then y = 42
- If x = 2, then y = 54
- If x = 3, then y = 66
- If x = 4, then y = 78
The only value of x that gives a positive integer value of y is x = 6, which gives y = 72.
Therefore, the total number of students in the class is 72.
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In a classroom there are certain number of benches. If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench, then, after accommodating all of them, space for 5 students is left. What is the total number of students in the class?a)30b)42c)72d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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In a classroom there are certain number of benches. If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench, then, after accommodating all of them, space for 5 students is left. What is the total number of students in the class?a)30b)42c)72d)None of theseCorrect answer is option 'C'. Can you explain this answer? for Teaching 2024 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about In a classroom there are certain number of benches. If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench, then, after accommodating all of them, space for 5 students is left. What is the total number of students in the class?a)30b)42c)72d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Teaching 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a classroom there are certain number of benches. If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench, then, after accommodating all of them, space for 5 students is left. What is the total number of students in the class?a)30b)42c)72d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
In a classroom there are certain number of benches. If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench, then, after accommodating all of them, space for 5 students is left. What is the total number of students in the class?a)30b)42c)72d)None of theseCorrect answer is option 'C'. Can you explain this answer? for Teaching 2024 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about In a classroom there are certain number of benches. If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench, then, after accommodating all of them, space for 5 students is left. What is the total number of students in the class?a)30b)42c)72d)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Teaching 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a classroom there are certain number of benches. If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed. However, if 7 students are made to sit on a bench, then, after accommodating all of them, space for 5 students is left. What is the total number of students in the class?a)30b)42c)72d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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