Students of a class are preparing for a drill and are made to stand in rows. If 4 students are extra in a row, then there would be 2 rows less. But there would be 4 more rows if 4 students are less in a row. The number of students in the class is
(a)56
(b)65
(c)69
(d)96
Answer
Answer (as printed): D
Explanation
Let the number of students in a row be $x$ and the total number of rows be $y$. Then, total number of students in the class $=x y$. $$\begin{aligned} & \therefore(x+4)(y-2)=x y \Rightarrow x y-2 x+4 y-8=x y \\ & \Rightarrow 2 x-4 y=-8 \Rightarrow x-2 y=-4 \end{aligned}$$ And, $(x-4)(y+4)=x y \Rightarrow x y+4 x-4 y-16=x y$ $$\Rightarrow 4 x-4 y=16 \Rightarrow x-y=4$$ Subtracting (i) from (ii), we get: $y=8$. Putting $y=8$ in (ii), we get: $x=12$. Hence, total number of students in the class $=x y=(12$ $\times 8)=96$.
Explanation as extracted from the printed page; notation may be imperfect.