Math Problem Statement

70% students passed Mathematics, 60% passed Science, and 20% passed both subjects. Additionally, 550 students failed both subjects. Determine: (1) the total number of students, (2) students passing only Mathematics, and (3) students passing only Science.

Solution

The image contains text with a mathematical problem written in Nepali. Let me extract and analyze it for solving the problem.The problem in the image discusses percentages and student data. Translating and summarizing the first problem (labeled 6 "क"), we have:

  • 70% students passed Mathematics.
  • 60% students passed Science.
  • 20% students passed both subjects.
  • 550 students failed in both subjects.

Tasks:

  1. Find the total number of students.
  2. Find the number of students passing only Mathematics.
  3. Find the number of students passing only Science.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Percentage Calculation
Union and Intersection of Sets

Formulas

Total students = n(A ∪ B) + n(neither)
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
Students failing both = Total students - n(A ∪ B)

Theorems

Principle of Inclusion-Exclusion

Suitable Grade Level

Grades 9-12

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