Question 72

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.

Solution

Let number of students in each row be $$x$$ and number of rows = $$y$$

=> Total number of students = $$xy$$ 

Case 1 : $$(x+4)\times(y-2)=xy$$

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

=> $$2y-x=4$$ ----------(i)

Case 2 : $$(x-4)\times(y+4)=xy$$

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

=> $$x-y=4$$ ------------(ii)

Adding equations (i) and (ii), => $$y=8$$

and similarly, $$x=12$$

$$\therefore$$ Total number of students = $$12\times8=96$$

=> Ans - (C)


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