Question

Students of a class are made to stand in rows. If 4 students are extra in a row, there would be 2 rows less. If 4 students are less in a row, there would be 4 more rows. Find the numberof students in the class.

• A. 86
• B. 106
• C. 96
• D. Cannot be determined

Answer 1

Answer: (C)

96

Answer 2

Assume the number of students in each row be $x$

the number of rows be $y$

So, the total number of students will be $x \times y$

According to Case number 1,

$(x + 4 ) \times (y - 2) = xy$

$xy - 2x + 4y - 8 = xy$

$2y - x = 4$ – (i)

According to Case number 2,

$(x - 4 ) \times (y + 4) = xy$

$xy + 4x - 4y - 16 = xy$

$x - y = 4$ – (ii)

By Adding the equation (i) and (ii) we get,

$y = 8$

Putting the value of $y$ in equation (ii)

$x$ = 8 + 4

$x = 12$

So, the total number of students will be 12 × 8

= 96

The correct option is (C): 96