Question

The students of a class are made to stand in rows. If 3 students are extra in a row, then there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.​

Answer 1

Answer:

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Step-by-step explanation:

here is your answer

Answer 2

Given :-

• If 3 students are extra in a row, then there would be 1 row less.

• If 3 students are less in a row, there would be 2 rows more.

To Find :-

• Total number of students.

Solution :-

Let the number of rows be x.

Number of students in a row will be y.

Then, total number of students in the class

= Number of students in a row × number of rows

= xy............. eq(1)

According to the question :

Given that,

If 3 students are extra in a row, then there would be 1 row less.

Therefore,

xy = ( x -1) ( y+3)

⟼ xy = xy +3x -y -3

⟼ 3x -y = 3.............. eq(2)

Again, given that

If 3 students are less in a row, there would be 2 rows more.

Therefore,

xy = (x+2) (y-3)

⟼ xy = xy -3x +2y -6

⟼ -3x +2y = 6..........eq(3)

Now, subtract eq (3) from eq(1)

3x -y = 3

-3x +2y = 6

__________

⟼ y =9

Put the value of y in eq(2)

3x -y = 3

⟼ 3 x -9 =3

⟼ 3x = 12

$⟼x = 4$

So, total number of students is = xy = 36

Number of rows = 4

Number of students in a row = 9