IPMAT 2025 Exam Solved Papers

The number of students who did not appear for the English exam is twice that of those who did not appear for the Math exam. Let us assume that the number of students who did not appear for Math = X, then the number of students who did not appear for English = 2XThe number of students who passed the Math exam is twice that of those who appeared but failed the English exam. Let us assume the number of students who appeared but failed the English exam is Y, then the number of students who passed the Math exam $=2 \mathrm{Y}$The number of students who passed the English exam is twice that of those who appeared but failed the Math exam. Let us assume that the number of students who appeared but failed the Math exam $=\mathrm{Z}$, then the number of students who passed the English exam = 2Z.$$\begin{aligned} & 2 X+2 Z+Y=120 \rightarrow 1 \\ & X+2 Y+Z=120 \rightarrow 2 \end{aligned}$$Multiply eq. 2 by 2, and subtract eq. 1 from it.$$\begin{aligned} & \Rightarrow(2 X+4 Y+2 Z)-(2 X+Y+2 Z)=240-120 \\ & \Rightarrow 3 Y=120 \\ & \Rightarrow Y=40 \end{aligned}$$