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

The Correct Option is C

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