Math Problem Statement

Questions:

  1. Assume that in MP A, 300 Students sat for Mathematics and Physics examination, 70 students failed in Mathematics and 80 failed in English of which 30 passed in Mathematics. How many students a. failed in both subjects b. passed in both subjects c. passed only in Mathematics d. failed in only in physics

Solution

To solve this problem, we will use the given data systematically and calculate step by step.

Given Data:

  1. Total number of students: 300300
  2. Students who failed in Mathematics: 7070
  3. Students who failed in Physics: 8080
  4. Students who failed in Physics but passed in Mathematics: 3030

Analysis and Solution:

a. Students who failed in both subjects:

  • Students who failed in Physics but passed in Mathematics: 3030.
  • Total students failing in Physics: 8080.
  • Therefore, students failing in both Physics and Mathematics = 80−30=5080 - 30 = 50.

b. Students who passed in both subjects:

  • Students who failed in Mathematics: 7070.
  • Students who failed in Physics: 8080.
  • Students failing in both: 5050.

Using the principle of inclusion-exclusion:
Students failing in at least one subject = 70+80−50=10070 + 80 - 50 = 100.
Thus, students passing in both subjects = 300−100=200300 - 100 = 200.

c. Students who passed only in Mathematics:

  • Students who failed in Mathematics: 7070, so students who passed in Mathematics = 300−70=230300 - 70 = 230.
  • Students who passed Mathematics but failed in Physics = 3030.

Students passing only in Mathematics = 230−30=200230 - 30 = 200.

d. Students who failed only in Physics:

  • Total students failing in Physics: 8080.
  • Students failing in both subjects: 5050.

Students failing only in Physics = 80−50=3080 - 50 = 30.

Final Answers:

a. Students failing in both subjects: 50
b. Students passing in both subjects: 200
c. Students passing only in Mathematics: 200
d. Students failing only in Physics: 30

Let me know if you want further clarifications or additional details!

Related Questions:

  1. What is the formula for calculating overlap in sets for multiple conditions?
  2. How would the answers change if total students were different?
  3. How can this be represented in a Venn diagram?
  4. What would happen if xx additional students failed in both subjects?
  5. How can we verify the results using percentages of students?

Tip:

Always double-check the total using inclusion-exclusion principles to ensure consistency in results.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Inclusion-Exclusion Principle
Basic Arithmetic

Formulas

Inclusion-Exclusion Principle: |A ∪ B| = |A| + |B| - |A ∩ B|
Total Passed = Total Students - Total Failed
Specific Category Calculation: e.g., Failed in Both = Failed in Subject 1 ∩ Failed in Subject 2

Theorems

Inclusion-Exclusion Principle

Suitable Grade Level

Grades 8-10

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