Class 10 Exam > Class 10 Questions > The student of a class are made to stand in r...
Start Learning for Free
The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?
- a)96
- b)106
- c)86
- d)116
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The student of a class are made to stand in rows. If 4 students are ex...
Let the number of rows be x and the number of students in each row be y.
Total number of students = xy
(x - 2) (y + 4) = xy
⇒ xy + 4x - 2y - 8 = xy
⇒ 4x - 2y = 8 ...(1)
and (x + 4) (y - 4) = xy
xy - 4x + 4y - 16 = xy
⇒ -4x + 4y = 16 ...(2)
From eqn. (1) and (2)
4x - 2y - 4x + 4y = 24
2y = 24 ⇒ y = 12
and 4x - 2 × 12 = 8
⇒ 4x = 8 + 24 = 32 ⇒ x = 8
Total no. of students = 12 × 8 = 96.
Total number of students = xy
(x - 2) (y + 4) = xy
⇒ xy + 4x - 2y - 8 = xy
⇒ 4x - 2y = 8 ...(1)
and (x + 4) (y - 4) = xy
xy - 4x + 4y - 16 = xy
⇒ -4x + 4y = 16 ...(2)
From eqn. (1) and (2)
4x - 2y - 4x + 4y = 24
2y = 24 ⇒ y = 12
and 4x - 2 × 12 = 8
⇒ 4x = 8 + 24 = 32 ⇒ x = 8
Total no. of students = 12 × 8 = 96.
Free Test
FREE
| Start Free Test |
Community Answer
The student of a class are made to stand in rows. If 4 students are ex...
Let's assume the number of students in each row is x and the number of rows is y.
Given that if 4 students are extra in each row, there would be 2 rows less, we can write the equation as:
(x + 4)(y - 2) = xy
Similarly, if 4 students are less in each row, there would be 4 rows more:
(x - 4)(y + 4) = xy
Simplifying these equations will help us find the values of x and y, which represent the number of students in each row and the number of rows, respectively.
Simplifying the first equation:
xy + 4y - 2x - 8 = xy
4y - 2x - 8 = 0
2y - x = 4 --(1)
Simplifying the second equation:
xy - 4x + 4y - 16 = xy
4y - 4x - 16 = 0
y - x = 4 --(2)
Now, we have a system of equations (1) and (2) that we can solve simultaneously to find the values of x and y.
Adding equations (1) and (2):
(2y - x) + (y - x) = 4 + 4
3y - 2x = 8 --(3)
Multiplying equation (2) by 2 and subtracting it from equation (3):
3y - 2x - 2y + 2x = 8 - 8
y = 0
Substituting the value of y = 0 into equation (2):
0 - x = 4
x = -4
Since the number of students and rows cannot be negative, this solution is not valid.
Therefore, there is no solution to the given system of equations, which means there is no consistent relationship between the number of students in each row and the number of rows. As a result, it is not possible to determine the number of students in the class.
Given that if 4 students are extra in each row, there would be 2 rows less, we can write the equation as:
(x + 4)(y - 2) = xy
Similarly, if 4 students are less in each row, there would be 4 rows more:
(x - 4)(y + 4) = xy
Simplifying these equations will help us find the values of x and y, which represent the number of students in each row and the number of rows, respectively.
Simplifying the first equation:
xy + 4y - 2x - 8 = xy
4y - 2x - 8 = 0
2y - x = 4 --(1)
Simplifying the second equation:
xy - 4x + 4y - 16 = xy
4y - 4x - 16 = 0
y - x = 4 --(2)
Now, we have a system of equations (1) and (2) that we can solve simultaneously to find the values of x and y.
Adding equations (1) and (2):
(2y - x) + (y - x) = 4 + 4
3y - 2x = 8 --(3)
Multiplying equation (2) by 2 and subtracting it from equation (3):
3y - 2x - 2y + 2x = 8 - 8
y = 0
Substituting the value of y = 0 into equation (2):
0 - x = 4
x = -4
Since the number of students and rows cannot be negative, this solution is not valid.
Therefore, there is no solution to the given system of equations, which means there is no consistent relationship between the number of students in each row and the number of rows. As a result, it is not possible to determine the number of students in the class.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?a)96b)106c)86d)116Correct answer is option 'A'. Can you explain this answer?
Question Description
The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?a)96b)106c)86d)116Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?a)96b)106c)86d)116Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?a)96b)106c)86d)116Correct answer is option 'A'. Can you explain this answer?.
The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?a)96b)106c)86d)116Correct answer is option 'A'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?a)96b)106c)86d)116Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?a)96b)106c)86d)116Correct answer is option 'A'. Can you explain this answer?.
Solutions for The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?a)96b)106c)86d)116Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?a)96b)106c)86d)116Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?a)96b)106c)86d)116Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?a)96b)106c)86d)116Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?a)96b)106c)86d)116Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The student of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less to each row, there would be 4 rows more. What is the number of students in the class?a)96b)106c)86d)116Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup