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In a mid-term exam of class 11, 42% students failed in Mathematics, 54% students failed in Physics and 48% students failed in Chemistry. Only 10% students failed in all the three subjects. 20% students failed in both Physics and Chemistry, 15% students failed in both Chemistry and Mathematics, and 18% students failed in both Physics and Mathematics. What is the percentage of those students who failed in two subjects only?

In a mid-term exam of class 11, 42% students failed in Mathematics, 54% students failed in Physics and 48% students failed in Chemistry. Only 10% students failed in all the three subjects. 20% students failed in both Physics and Chemistry, 15% students failed in both Chemistry and Mathematics, and 18% students failed in both Physics and Mathematics. What is the percentage of those students who failed in two subjects only? Correct Answer 23%

Given:

In a mid-term exam of class 11, 42% of students failed in Mathematics, 54% of students failed in Physics and 48% of students failed in Chemistry. Only 10% of students failed in all three subjects. 20% of students failed in both Physics and Chemistry, 15% of students failed in both Chemistry and Mathematics, and 18% of students failed in both Physics and Mathematics. 

Concept used:

Venn Diagram

Calculation:

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Here, Mathematics, Physics, and Chemistry are denoted by M, P, and C respectively.

According to the question,

M = 42%

P = 54%

C = 48%

M + P + C = 10%

M + C = 15%

P + M = 18%

P + C = 20%

Hence,

Only (M + C) = 15 - 10 = 5%

Only (P + M) = 18 - 10 = 8%

Only (P + C) = 20 - 10 = 10%

Thus,  the percentage of those students who failed in two subjects only = 5 + 8 + 10 = 23%

∴ The percentage of those students who failed in two subjects only is 23%.

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