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.

Updated On: Oct 4, 2024
  • 86
  • 106
  • 96
  • Cannot be determined
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The Correct Option is C

Solution and Explanation

Assume the number of students in each row be xx

the number of rows be yy

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

According to Case number 1,

(x+4)×(y2)=xy(x + 4 ) \times (y - 2) = xy

xy2x+4y8=xyxy - 2x + 4y - 8 = xy

2yx=42y - x = 4 – (i)

 According to Case number 2,

(x4)×(y+4)=xy(x - 4 ) \times (y + 4) = xy

xy+4x4y16=xyxy + 4x - 4y - 16 = xy

xy=4x - y = 4 – (ii)

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

y=8y = 8

Putting the value of yy in equation (ii)

xx = 8 + 4

x=12x = 12

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

= 96

The correct option is (C): 96

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