The English and Math exams were conducted separately for a class of 120 students.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. The number of students who passed the Math exam is twice that of those who appeared but failed the English exam. If the number of students who passed the English exam is twice the number of students who appeared but failed the Math exam, then the number of students who appeared but failed the English exam is ________

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 = 2X

The 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 = 2Y

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 = Z, then the number of students who passed the English exam = 2Z.

$$2X+2Z+Y=120\rightarrow1$$

$$X+2Y+Z=120\rightarrow2$$

Multiply eq. 2 by 2, and subtract eq. 1 from it.

=> $$(2X+4Y+2Z)-(2X+Y+2Z)=240-120$$

=> $$3Y=120$$

=> $$Y=40$$