The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row there would be 2 rows more. Find the number of student in the class.
Answers
Given :
The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row there would be 2 rows more.
Solution:
Let the number of rows be y and number of students in a row be x
Total students of the class = Number of rows × Number of students in a row
Total students of the class = xy
Condition I:
Total number of students = (y - 1) (x + 3)
xy = (y - 1) (x + 3)
xy = xy - x + 3y-3
3y − x-3 = 0
3y − x= 3
-x + 3y = 3…………,...(1)
Condition II:
Total number of students = (y + 2) (x − 3)
xy = xy + 2x -3 y − 6
2x− 3y = 6………….. (2)
On multiplying equation (1) by (2) :
2(-x + 3y = 3)
-2x + 6y = 6……………….(3)
On adding equation 2 and 3 :
2x − 3y = 6
-2x + 6y = 6
--------------------
3y = 12
y = 12/3
y = 4
On putting y = 4 in eq 1 :
-x + 3y = 3
-x + 3(4) = 3
-x + 12 = 3
-x = 3 - 12
-x = - 9
x = 9
Number of students in class= xy = 9 × 4 = 36.
Hence, the number of students in class = 36
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Answer:
Step-by-step explanation:
Solution :-
Let the number of rows be x
And a number of students in a row be y.
Total students of the class = xy
According to the Questions,
⇒ xy = (x − 1) (y + 3) = xy − y + 3x − 3
⇒ 3x − y − 3 = 0
⇒ 3x − y = 3 ....(i)
⇒ xy = xy + 2y − 3x − 6
⇒ 3x − 2y = −6 (2)
Solving Eq (i) and (ii), we get
⇒ (3x − y) − (3x − 2y) = 3 − (−6)
⇒ − y + 2y = 3 + 6
⇒ y = 9
Putting y's value in Eq (i), we get
⇒ 3x − 9 = 3
⇒ 3x = 9 + 3 = 12
⇒ x = 4
Number of rows = x = 4
Number of students in a row = y = 9
Total students in a class = xy = 4 × 9 = 36