The following table gives the details of the number of students in Class 10 section A and B who had taken the mid-term and final exams. The percentage of students in section A is _____ (round of one decimal). Result Sec A Sec B Total number of students who failed in both exams 28 23 Total number of students who failed in mid-term but passed in finals 14 12 Total number of students who passed in mid-term but failed in finals 6 17 Total number of students who passed in both the exams 64 55
51.4
Calculating the Percentage of Students in Section A
The question asks us to find the percentage of students in Section A out of the total number of students across both Section A and Section B. We are provided with a table detailing the results of students in mid-term and final exams for both sections.
First, let's understand the data provided in the table:
| Result | Sec A | Sec B |
|---|---|---|
| Total number of students who failed in both exams | 28 | 23 |
| Total number of students who failed in mid-term but passed in finals | 14 | 12 |
| Total number of students who passed in mid-term but failed in finals | 6 | 17 |
| Total number of students who passed in both the exams | 64 | 55 |
To find the percentage of students in Section A, we need two key pieces of information:
- The total number of students in Section A.
- The total number of students in both Section A and Section B combined.
Step-by-Step Calculation
1. Calculate the Total Number of Students in Section A
We sum the number of students in Section A from all result categories:
Total students in Sec A = (Failed in both) + (Failed mid, Passed final) + (Passed mid, Failed final) + (Passed both)
Total students in Sec A = $28 + 14 + 6 + 64$
Total students in Sec A = $112$
2. Calculate the Total Number of Students in Section B
We sum the number of students in Section B from all result categories:
Total students in Sec B = (Failed in both) + (Failed mid, Passed final) + (Passed mid, Failed final) + (Passed both)
Total students in Sec B = $23 + 12 + 17 + 55$
Total students in Sec B = $107$
3. Calculate the Total Number of Students in Both Sections
We add the total students from Section A and Section B:
Total students (Sec A + Sec B) = Total students in Sec A + Total students in Sec B
Total students (Sec A + Sec B) = $112 + 107$
Total students (Sec A + Sec B) = $219$
4. Calculate the Percentage of Students in Section A
The percentage of students in Section A is calculated by dividing the total number of students in Section A by the total number of students in both sections and multiplying by 100. The formula is:
Percentage of students in Sec A = $\left( \frac{\text{Total students in Sec A}}{\text{Total students in Sec A + Sec B}} \right) \times 100\%$
Percentage of students in Sec A = $\left( \frac{112}{219} \right) \times 100\%$
Let's perform the calculation:
$\frac{112}{219} \approx 0.5114155...$
Percentage of students in Sec A $\approx 0.5114155... \times 100\%$
Percentage of students in Sec A $\approx 51.14155...\%$
5. Round the Percentage to One Decimal Place
The question asks us to round the percentage to one decimal place. Rounding $51.14155...\%$ to one decimal place gives $51.1\%$.
Based on the calculation using the provided table data, the percentage of students in Section A is approximately 51.1%.
Among the given options, option 2 is 51.4%.
Revision Table: Key Calculations
| Metric | Calculation | Value |
|---|---|---|
| Total students in Sec A | $28 + 14 + 6 + 64$ | $112$ |
| Total students in Sec B | $23 + 12 + 17 + 55$ | $107$ |
| Total students (Sec A + Sec B) | $112 + 107$ | $219$ |
| Percentage of students in Sec A | $\left( \frac{112}{219} \right) \times 100\%$ | $\approx 51.14\%$ |
| Percentage rounded to one decimal | Rounding $51.14\%$ to one decimal | $51.1\%$ |
Additional Information: Understanding Percentages
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, '%', or the abbreviations 'pct.', 'pct'. Sometimes the abbreviation 'pc' is also used. Percentages are used to express how large one quantity is in relation to another quantity; the second quantity is the base or the whole, which is considered as 100%.
In this problem, the 'whole' is the total number of students in both sections, and the 'part' is the number of students in Section A. We calculate what percentage the 'part' is of the 'whole'.
The formula for calculating percentage is universally applied:
Percentage = $\left( \frac{\text{Part}}{\text{Whole}} \right) \times 100\%$
Rounding is necessary when the result of a calculation has more decimal places than required by the question. Rounding to one decimal place means keeping one digit after the decimal point and adjusting it based on the value of the second digit:
- If the second digit is 5 or greater, round up the first digit.
- If the second digit is less than 5, keep the first digit as it is.
For example, 51.14 rounded to one decimal place is 51.1 because the second digit (4) is less than 5. If the number was 51.16, it would round to 51.2.
Similar Questions
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Direction: Study the table given below and answer the following question.
City
Population
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% of literates
A
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150
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