Question

Consider the Diagram. 500 Candidates appeared in an Examination comprising test in English, Hindi and Maths. The Diagram gives number of students who failed in different tests. What is the percentage of student who failed at least two subjects?

• A. \( 6.8 \)
• B. \( 7.8 \)
• C. \( (A)0 \)
• D. \( 0.078 \)

Hint:

\textbf{Venn Diagrams and Percentage Calculations.} When dealing with Venn diagrams and percentages, carefully identify the regions corresponding to the conditions given in the question. For "at least two" conditions, include those who satisfy the condition for exactly two as well as more than two categories. The percentage is then calculated by dividing the relevant number of students by the total number of students and multiplying by 100.

Answer 1

The Correct Option is B

The Venn diagram shows the number of students who failed in different combinations of English, Hindi, and Maths. We need to find the percentage of students who failed in at least two subjects. This means we need to count the number of students who failed in exactly two subjects or in all three subjects. From the Venn diagram:
Students who failed in English and Hindi only: 10
Students who failed in Hindi and Maths only: 12
Students who failed in English and Maths only: 12
Students who failed in English, Hindi, and Maths: 5 The number of students who failed in at least two subjects is the sum of those who failed in exactly two subjects and those who failed in all three subjects: Number of students failed in at least two subjects \( = (\text{English and Hindi only}) + (\text{Hindi and Maths only}) + (\text{English and Maths only}) + (\text{English, Hindi, and Maths}) \) Number of students failed in at least two subjects \( = 10 + 12 + 12 + 5 = 39 \) The total number of candidates who appeared in the examination is 500. The percentage of students who failed in at least two subjects is: $$ \text{Percentage} = \frac{\text{Number of students failed in at least two subjects}}{\text{Total number of candidates}} \times 100 $$ $$ \text{Percentage} = \frac{39}{500} \times 100 $$ $$ \text{Percentage} = \frac{39}{5} $$ $$ \text{Percentage} = 7.8 $$ Therefore, the percentage of students who failed in at least two subjects is \( 7.8 \).