In the given chart which of the following represents the number of students who study more than one subjects (Hindi or Maths or English)?
Show Hint
Be careful with the phrasing! "More than one" strictly means 2 or more. Always exclude the outer, non-overlapping regions representing single subjects when solving such problems.
• Step 1: Understanding the Question: This question is based on Venn diagram analysis. We are asked to find the total number of students who are studying more than one subject. "More than one subject" means studying exactly two subjects or all three subjects.
• Step 2: Key Formula or Approach:
In a 3-set Venn diagram representing sets \(M\) (Maths), \(H\) (Hindi), and \(E\) (English):
The regions representing students studying "more than one subject" are the intersections of the sets:
- Students studying Maths and Hindi only
- Students studying Maths and English only
- Students studying Hindi and English only
- Students studying all three subjects (Maths, Hindi, and English)
We sum the numbers corresponding to these four intersecting regions.
• Step 3: Detailed Explanation:
Let us observe the given Venn diagram:
- The region containing 5 represents the intersection of Mathematics and Hindi (but not English).
- The region containing 15 represents the intersection of Mathematics and English (but not Hindi).
- The region containing 10 represents the intersection of Hindi and English (but not Mathematics).
- The region containing 20 at the center represents the intersection of all three subjects (Mathematics, Hindi, and English).
Now, let us calculate the total sum of these intersection regions:
\[ \text{Total students studying } > 1 \text{ subject} = 5 + 15 + 10 + 20 \]
\[ \text{Total} = 50 \]
Let us verify that we did not include any single-subject student:
- Only Mathematics = 25 (Excluded)
- Only Hindi = 15 (Excluded)
- Only English = 35 (Excluded)
These are excluded because they study only one subject.
Hence, the calculated sum of 50 is correct.
• Step 4: Final Answer: The number of students studying more than one subject is 50, which corresponds to option (D).
