IPMAT Indore 2025 (SA) - English exam and Math exam were conducted separately for a class of 120 students. The number of students who did not appear for the English exam is twice the number of students who did not appear for the Math exam. The number of students who passed the Math exam is twice the number of students 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 ________ | PYQs + Solutions | AfterBoards
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IPMAT Indore 2025

Modern Math
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Set Theory

Medium

English exam and Math exam were conducted separately for a class of 120 students. The number of students who did not appear for the English exam is twice the number of students who did not appear for the Math exam. The number of students who passed the Math exam is twice the number of students 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 ________

Entered answer:

✅ Correct Answer: 40
- Students who didn't appear for Math: xx \newline - Students who didn't appear for English: 2x2x (as given) \newline - Students who appeared but failed English: yy (this is what we need to find) \newline - Students who appeared but failed Math: zz \newline - Students who passed Math: 2y2y (given) \newline - Students who passed English: 2z2z (given)
For each exam, we can calculate the number of students who appeared: \newline - Students who appeared for Math: 120−x120 - x \newline - Students who appeared for English: 120−2x120 - 2x
The students who appeared can be split into those who passed and those who failed: \newline - For Math: (120−x)=2y+z(120 - x) = 2y + z \newline - For English: (120−2x)=2z+y(120 - 2x) = 2z + y
From the second equation: \newline y=120−2x−2zy = 120 - 2x - 2z
Substitute this into the first equation:
(120−x)=2(120−2x−2z)+z(120 - x) = 2(120 - 2x - 2z) + z
(120−x)=240−4x−4z+z(120 - x) = 240 - 4x - 4z + z
(120−x)=240−4x−3z(120 - x) = 240 - 4x - 3z
−x+4x=240−120−3z-x + 4x = 240 - 120 - 3z
3x=120−3z3x = 120 - 3z
x=40−zx = 40 - z
Substitute back to find yy:
y=120−2x−2zy = 120 - 2x - 2z
y=120−2(40−z)−2zy = 120 - 2(40 - z) - 2z
y=120−80+2z−2zy = 120 - 80 + 2z - 2z
y=40y = 40
Therefore, the number of students who appeared but failed the English exam is 4040.

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