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?

The correct option is 7.8%.

Step-by-step Explanation:

To find the percentage of students who failed in at least two subjects, we need to analyze the Venn diagram provided in the image, which displays the number of candidates who failed in three different subjects: English, Hindi, and Math.

1. Identify the total number of candidates:
The total number of candidates who appeared in the examination is given as 500.

2. Determine the number of students who failed in at least two subjects:
Failing in "at least two subjects" means a student failed in either exactly two subjects or in all three subjects. From the Venn diagram, we identify the overlapping regions (intersections) of the circles:
- Candidates who failed in English and Hindi (but not Math) = 10
- Candidates who failed in English and Math (but not Hindi) = 12
- Candidates who failed in Hindi and Math (but not English) = 12
- Candidates who failed in all three subjects (English, Hindi, and Math) = 5

Now, we sum these values to find the total number of candidates who failed in at least two subjects:

$$\text{Number of candidates}=10+12+12+5=39$$

3. Calculate the percentage:
To find the percentage of these students relative to the total number of candidates (500), we use the percentage formula:

$$\text{Percentage}=\left(\frac{\text{Number of students who failed at least 2 subjects}}{\text{Total number of candidates}}\right)\times 100$$

Substituting the values into the formula:

$$\text{Percentage}=\left(\frac{39}{500}\right)\times 100$$

Simplifying the calculation:

$$\text{Percentage}=\frac{39}{5}=7.8\%$$

Therefore, the percentage of students who failed in at least two subjects is 7.8%.