In an examination, 92% of the students passed and 480 students failed. If so, how many students appeared in the examination?
6000
Understanding the Examination Result Problem
This question asks us to find the total number of students who participated in an examination. We are given the percentage of students who passed and the specific number of students who failed. To solve this, we first need to figure out what percentage of students failed the examination.
Calculating the Percentage of Failed Students
In any examination, the total percentage of students appearing is 100%. Students either pass or fail. Therefore, the percentage of students who failed is the total percentage minus the percentage of students who passed.
- Total percentage of students = 100%
- Percentage of students who passed = 92%
- Percentage of students who failed = Total percentage - Percentage of students who passed
- Percentage of students who failed = 100% - 92% = 8%
So, 8% of the students who appeared for the examination failed.
Relating Percentage Failed to Number Failed
We are given that 480 students failed the examination. We now know that this number represents 8% of the total number of students who appeared.
Let 'T' be the total number of students who appeared in the examination.
According to the problem:
8% of T = 480
Solving for the Total Number of Students
To find the total number of students (T), we can write the percentage as a fraction:
$\frac{8}{100} \times T = 480$
Now, we need to isolate T. We can do this by multiplying both sides of the equation by $\frac{100}{8}$:
$T = 480 \times \frac{100}{8}$
We can simplify the calculation by dividing 480 by 8:
$480 \div 8 = 60$
So, the equation becomes:
$T = 60 \times 100$
$T = 6000$
Therefore, the total number of students who appeared in the examination was 6000.
Verification of the Solution
Let's check if our answer is correct. If there were 6000 students in total, and 8% failed, the number of failed students would be:
$8\% \text{ of } 6000 = \frac{8}{100} \times 6000 = 8 \times 60 = 480$
This matches the number of failed students given in the question (480). Also, 92% passed:
$92\% \text{ of } 6000 = \frac{92}{100} \times 6000 = 92 \times 60 = 5520$
Total students = Passed students + Failed students = $5520 + 480 = 6000$. This confirms our total is correct.
| Category | Percentage | Number of Students |
|---|---|---|
| Passed | 92% | $92\% \text{ of } 6000 = 5520$ |
| Failed | 8% (100% - 92%) | 480 (Given) |
| Total | 100% | $5520 + 480 = 6000$ |
The calculation confirms that if 6000 students appeared, 480 students failing corresponds to 8% failure rate, which is consistent with a 92% pass rate.
Revision Table: Examination Student Calculation
| Concept | Formula / Calculation | Value |
|---|---|---|
| Percentage Passed | Given | 92% |
| Number Failed | Given | 480 |
| Percentage Failed | 100% - Percentage Passed | $100\% - 92\% = 8\%$ |
| Total Students (T) | Percentage Failed of T = Number Failed | $\frac{8}{100} \times T = 480$ |
| Total Students (T) | $T = \frac{\text{Number Failed}}{\text{Percentage Failed}} \times 100$ | $T = \frac{480}{8} \times 100 = 60 \times 100 = 6000$ |
Additional Information: Percentage Calculations in Exams
Understanding percentages is crucial for solving many problems related to examinations and results. Here are some key points:
- Total is always 100%: When dealing with percentages of a whole (like students in an exam), the total represents 100%.
- Complementary Percentages: If students are divided into categories like 'passed' and 'failed', their percentages add up to 100%. For example, if 92% passed, $100\% - 92\% = 8\%$ must have failed.
- Finding the Whole from a Part: If you know the percentage that a certain number represents, you can find the total (the whole). The formula is:
$\text{Total} = \frac{\text{Part (Number)}}{\text{Percentage (in decimal or fraction)}} = \frac{\text{Part}}{\text{Percentage}} \times 100$ - Finding a Part from the Whole: If you know the total and a percentage, you can find the number that represents that percentage:
$\text{Part (Number)} = \text{Percentage (in decimal or fraction)} \times \text{Total} = \frac{\text{Percentage}}{100} \times \text{Total}$
These basic concepts help in tackling various percentage-based problems efficiently.
Similar Questions
Chamanlal, Arshad and Jagit Singh contested an election. All the votes polled were valid. Arshad got 35% of the total votes. For every 35 votes Chamanlal got 14 votes. The winner got 4950 more votes than the person who received the least number of votes. Find the total number of votes polled.
A father gives 8% of his monthly income to both his sons as pocket money. The elder son gets 85% of the total amount given to both sons. He spends 90% of the amount and saves Rs. 17. What is the monthly income of his father?
In an examination a candidate had to sit for three papers A, B, and C. The candidate secured 75% marks in Paper A, 80% marks in Paper B, and 60% marks in Paper C. If the weightage assigned to Papers A, B, and C were 40%, 50% and 10%, respectively, then find the weighted percentage of marks obtained by the candidate, when all the three papers were taken together.
The sum of two numbers is 680. If the bigger number is decreased by 15% and the smaller number is increased by 15%, then the resultant numbers are equal. Find the smaller number.
The ratio of the cost price and selling price of an article is 10 ∶ 11. The gain per cent is:
A number is decreased by 20% to get another number. The number so obtained is increased by 200% to get a third number. The difference of the third number and the original number is what percentage more or less than the difference of second and the third number?
In the first year the population of a town decreased by 5% due to the Corona virus first wave. In the next year it decreased again by 5% due to the second wave and in the third year it increased by 5%. At the end of the third year the population was 9,47,625. What was the population at the beginning of the first year?
In an election between two candidates, a candidate who gets 64% of the votes polled is elected by a majority of 252 votes. What is the total number of votes polled?
Out of an earning of Rs. 720, Pankaj spends 65%. How much does he save?
The number of units manufactured by a company A was 12500 units in 2019 and 10625 units in 2020. While in company B, the production fell from 34000 units in 2019 to 30600 units in 2020. If X and Y are the percentage decrease in the number of units manufactured by company A and B respectively from 2019 to 2020, then what will be the ratio of X and Y?
Important Questions from Percentage
In an examination, 25% of the candidates failed in Mathematics and 12% failed in English. If 10% of the candidates failed in both the subjects and 292 candidates passed in both the subjects, which one of the following is the number of total candidates appeared in the examination?
What is the value of 9% of 5500 + 2.4% of 1100 - 40% of 1600?
Population of a village is 7960 in which 4660 are female. If in that village 60% are literate in which 70% female are literate, then what is the number of literate male ?
The numbers of students of three classes of a school are in the ratio 4 : 5 : 6. If numbers of students in these classes increase by 25%, 20% and 25% respectively, then ratio of numbers of students will become:
In an examination, Ram obtained 20 % more than Ashok but 10% less than Rajesh. If the marks obtained by Ashok is 1080. Then the Percentage marks obtained by Rajesh if the full marks is 2000 ;
