Question

A class has 175 students. The following data shows the number of students opting for one or more subjects. Maths = 100, Physics = 70, Chemistry = 40, Maths and Physics = 30, Maths and Chemistry = 28, Physics and Chemistry = 23, Maths, Physics, and Chemistry = 18.
How many have offered Maths alone?

• A. 35
• B. 48
• C. 60
• D. 22

Hint:

Use the inclusion-exclusion principle to find the number of students opting for a specific subject, and subtract those opting for multiple subjects.

Answer 1

The Correct Option is C

Step 1: Use the principle of inclusion-exclusion to find the number of students who have offered Maths alone. The formula for inclusion-exclusion is: \[ |A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \cap C| + |A \cap B \cap C|. \] 
Let: - \( A \) be the set of students who opted for Maths, 
- \( B \) be the set of students who opted for Physics, 
- \( C \) be the set of students who opted for Chemistry. 
We are given: - \( |A| = 100, \quad |B| = 70, \quad |C| = 40, \) - \( |A \cap B| = 30, \quad |A \cap C| = 28, \quad |B \cap C| = 23, \quad |A \cap B \cap C| = 18 \). 
Step 2: Find the number of students who opted for Maths alone: \[ |A { alone}| = |A| - (|A \cap B| + |A \cap C| - |A \cap B \cap C|). \] Substitute the values: \[ |A { alone}| = 100 - (30 + 28 - 18) = 100 - 40 = 60. \]