Students of a class are preparing for a drill and are made to stand in rows. If 4 students are extra in a row, then there would be 2 rows less. But there would be 4 more rows if 4 students are less in a row. The number of students in the class is (a) 56 (b) 65 (c) 69 (d) 96

Explanation

Let the number of rows be x and the number of students in each row be y.
Then, the total number of students = xy .
Case I When there are 4 more students in each row = ( y + 4)
And, number of rows = (x - 2 )
Total number of students = (x - 2) ( y + 4)
`therefore (x - 2) ( y + 4) = xy rArr 4x - 2y = 8 `
`" " rArr 2 x - y = 4 " " `... (i)
Case II When 4 students are removed from each row.
Then, number of students in each row = ( y - 4)
And, number of rows = ( x+ 4)
Total number of stuents = ( x+ 4 ) ( y - 4)
` therefore (x + 4 ) ( y - 4) = xy rArr 4 y - 4x = 16`
`" " rArr 4 ( y - x) = 16 `
` " " rArr ( y - x ) = 4 " " `... (ii)
Adding (i) and (ii), we get x = 8
Putting ` x = 8` in (ii), we get
` y- 8 = 4 rArr y = 12 `
Thus, x = 8 and y = 12
This shows that there are 8 rows and there are 12 students in each row.
Hence, the number of students in the class = ` xy = 8 xx 12 = 96`.