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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?
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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.
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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.
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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?
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