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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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Verified Answer
In a classroom there are certain number of benches. If 6 students are ...
Let the total number of students in class be N.
No. of benches be x.
Given,
⇒ N = 6x + 6
⇒ N = 7x - 5
Then,
⇒ 6x + 6 = 7x - 5
⇒ x = 11
∴ Total number of Students = 6 × 11 + 6 = 72
Most Upvoted Answer
In a classroom there are certain number of benches. If 6 students are ...
Given:
- If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed.
- If 7 students are made to sit on a bench, then after accommodating all of them, space for 5 students is left.
To find:
- The total number of students in the class.
Solution:
Let's assume there are 'x' benches in the classroom and the total number of students is 'y'.
Case 1:
- If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed.
- In this case, we can assume that all benches are occupied except the last bench, which will have 5 students.
So, the total number of benches required in this case would be (x-1) and the total number of students would be 6(x-1) + 5.
Case 2:
- If 7 students are made to sit on a bench, then after accommodating all of them, space for 5 students is left.
- In this case, we can assume that all benches are fully occupied with 7 students except the last bench, which will have 5 students.
So, the total number of benches required in this case would be x and the total number of students would be 7x - 5.
Since both the cases represent the same total number of students, we can equate their expressions.
6(x-1) + 5 = 7x - 5
6x - 6 + 5 = 7x - 5
6x - 1 = 7x - 5
7x - 6x = 5 - 1
x = 4
Substituting the value of x in either of the expressions to find the total number of students:
Total number of students = 7x - 5
Total number of students = 7(4) - 5
Total number of students = 28 - 5
Total number of students = 23
Therefore, the total number of students in the class is 23.
- If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed.
- If 7 students are made to sit on a bench, then after accommodating all of them, space for 5 students is left.
To find:
- The total number of students in the class.
Solution:
Let's assume there are 'x' benches in the classroom and the total number of students is 'y'.
Case 1:
- If 6 students are made to sit on a bench, then to accommodate all of them, one more bench is needed.
- In this case, we can assume that all benches are occupied except the last bench, which will have 5 students.
So, the total number of benches required in this case would be (x-1) and the total number of students would be 6(x-1) + 5.
Case 2:
- If 7 students are made to sit on a bench, then after accommodating all of them, space for 5 students is left.
- In this case, we can assume that all benches are fully occupied with 7 students except the last bench, which will have 5 students.
So, the total number of benches required in this case would be x and the total number of students would be 7x - 5.
Since both the cases represent the same total number of students, we can equate their expressions.
6(x-1) + 5 = 7x - 5
6x - 6 + 5 = 7x - 5
6x - 1 = 7x - 5
7x - 6x = 5 - 1
x = 4
Substituting the value of x in either of the expressions to find the total number of students:
Total number of students = 7x - 5
Total number of students = 7(4) - 5
Total number of students = 28 - 5
Total number of students = 23
Therefore, the total number of students in the class is 23.
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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 Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways 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 Railways 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 Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways 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 Railways 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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