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Question 77

Students of a class are made to stand in rows. If 4 students are extra in each row, then there would be 2 rows less. If 4 students are less in each row, then there would be 4 more rows. The number of students in the class is

Solution

Let, the number of rows = 'x' and the number of students in the row be 'y'

Given that, if 4 students are extra in each row, then there would be 2 rows less,

(x - 2)(y + 4) = xy

xy + 4x -2y -8 = xy (or) 4x - 2y = 8 ...........(1)

If 4 students are less in each row, then there would be 4 more rows,

(x + 4)(y - 4) = xy

xy - 4x + 4y - 16 = xy (or) 4x - 4y = -16 .......(2)

Subtract equations (1) and (2)

2y = 24 (or) y =12

Substitute value of 'y' in equation (1)

4x - 2(12) = 8 $$\Rightarrow$$ 4x = 8 + 24 $$\Rightarrow$$ x = 8

Number of students in the class = xy $$\Rightarrow$$ 8 x 12 = 96

Hence, option D is the correct answer.

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