What is the percentage of candidates who failed in only one subject?

Question

Prepp Team · Accepted Answer

Understanding the Examination Failure Data

The problem provides data about the failure rates of 500 candidates in an examination consisting of three subjects: English, Hindi, and Mathematics. We are given specific numbers for candidates who failed in only one subject, in two subjects, and in all three subjects.

Here is a breakdown of the given information:

Total candidates appeared: 500
Failed in English only: 30
Failed in Hindi only: 75
Failed in Mathematics only: 50
Failed in both English and Hindi (includes those who failed in all three): 15
Failed in both Hindi and Mathematics (includes those who failed in all three): 17
Failed in both Mathematics and English (includes those who failed in all three): 17
Failed in all three tests: 5

Calculating Candidates Failing in Only One Subject

The question specifically asks for the percentage of candidates who failed in only one subject. The data directly provides the number of candidates who failed in only English, only Hindi, and only Mathematics. We just need to sum these numbers.

Number of candidates who failed in only one subject = (Failed in English only) + (Failed in Hindi only) + (Failed in Mathematics only)

Substituting the given values:

Number of candidates who failed in only one subject = 30 + 75 + 50

Number of candidates who failed in only one subject = 155

Calculating the Percentage

To find the percentage of candidates who failed in only one subject, we divide the number of candidates who failed in only one subject by the total number of candidates and multiply by 100.

Total candidates = 500

Number of candidates failing in only one subject = 155

Percentage of candidates failing in only one subject $= \left( \frac{\text{Number of candidates failing in only one subject}}{\text{Total candidates}} \right) \times 100$

Percentage $= \left( \frac{155}{500} \right) \times 100$

Let's perform the calculation:

Percentage $= 0.31 \times 100$

Percentage $= 31\%$

Therefore, 31% of the candidates failed in only one subject.

Step-by-Step Summary

Here's a summary of the steps taken to arrive at the solution:

Identify the number of candidates failing in only English (30).
Identify the number of candidates failing in only Hindi (75).
Identify the number of candidates failing in only Mathematics (50).
Sum these numbers to find the total number of candidates failing in only one subject: $30 + 75 + 50 = 155$.
Identify the total number of candidates: 500.
Calculate the percentage: $\left( \frac{155}{500} \right) \times 100 = 31\%$.

Failure Category	Number of Candidates
Failed in English only	30
Failed in Hindi only	75
Failed in Mathematics only	50
Total failed in only one subject	155
Total candidates	500

The percentage of candidates who failed in only one subject is 31%.

Revision Table: Key Concepts in Percentage Calculation

Concept	Description	Formula
Percentage	A way to express a number as a fraction of 100.	Percentage $= \frac{\text{Part}}{\text{Whole}} \times 100$
Calculating Part from Percentage	Finding the numerical value of a percentage of a given whole.	Part $= \frac{\text{Percentage}}{100} \times \text{Whole}$
Calculating Whole from Percentage	Finding the total when a part and its percentage are known.	Whole $= \frac{\text{Part}}{\text{Percentage}} \times 100$

Additional Information: Venn Diagrams and Set Theory in Exam Analysis

While this specific question could be solved by directly using the 'only one subject' numbers, the full dataset presented often relates to problems that can be solved using Venn diagrams and principles of set theory. Understanding how to represent overlapping sets (candidates failing in multiple subjects) is crucial for solving related questions, such as finding the number of candidates who failed in exactly two subjects, or the number of candidates who failed in at least one subject.

Key terms used in such problems:

Failed in A only: Candidates who failed only in subject A, and no other subject.
Failed in A and B: Candidates who failed in both subject A and subject B. This number usually includes those who failed in all three subjects unless specified as 'only A and B'.
Failed in A and B only: Candidates who failed in subject A and subject B, but not in the third subject.
Failed in at least one subject: Candidates who failed in one or more subjects (sum of those failing in only one, exactly two, and all three).
Failed in none: Candidates who passed all subjects (Total candidates - Failed in at least one subject).

For problems involving failures in two or three subjects, a Venn diagram helps visualize the overlaps and correctly calculate the numbers in each section (only A, only B, only C, only A&B, only B&C, only C&A, all A&B&C, none).