Question

The students present in an auditorium are asked to stand in rows. If there were 4 students extra in a row there would be 4 less rows. However, if 2 students were less in a row, there would be 4 more rows. The number of students present in the auditorium is

• A. 80
• B. 96
• C. 100
• D. 128

Answer 1

Answer: (B)

96

Answer 2

Let there are r rows and $x$ students in each row
According to question
(x$$+4)(r−4) = $x$×r
$⇒$ −4x$$+4r = 16 ………..(i)
($x$−2) $\times$(r$+$4) = $x$×r
4$x$−2r = 8 …………..(ii)
Adding equations (i) and (ii), we get
2r = 24
r = 12
4$x$−24 = 8
$x$=8.
Total number of students = 8×12 = 96.
So, the correct option is (B)