Question

students of a class r made to stand in rows .if 3dtudents r extra in a row there would be 1 row less .if 3 students r less in a row there would be 2vriws more .find the total no.of stdnts im d class

Answer 1

HEY!
________

Let total number of students in each row be x
Let the total number of rows be y
Total students = xy

Now, according to the question

CASE 1

New number of students in each row = (x + 3)
New number of rows = (y - 1)
So, total students = (x + 3)(y - 3)
But the number of students were xy

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

xy - x + 3y - 3 = xy

-x + 3y - 3 = xy - xy

-x + 3y - 3 = 0

-x + 3y = 3 ---------------------- (i)

CASE 2

New number of students in each row = (x - 3)
New number of rows = (y + 2)
So, Total students = (x - 3)(y + 2)
But the total number of students were xy

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

xy + 2x -3y - 6 = xy

2x - 3y - 6 = xy - xy

2x - 3y = 6 ------------------------------- (ii)

Now, on multiplying equation (i) by 2, we get,

- 2x + 6y = 6 -------–––––– (iii)

Now, adding (ii) and (iii)

2x - 3y = 6
-2x + 6y = 6
-------------------
3y = 12
-------------------

y = 4 ---------- [put in (ii)]

2x - 3(4) = 6

2x -12 = 6

2x = 18

x = 9

So, x = 9 and y = 4

Total number of students = xy

= 9 × 4

= 36

Therefore, total number of students are 36