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
In south, what is the percentage of seats won by party A (round to one decimal)?
Direction: Study the table given below and answer the following question.
City
Population
Literate
Illiterate
% of literates
A
200
150
50
-
B
-
200
100
66.6
C
150
50
100
-
D
120
-
90
25
Based on the given data, the percentage of literates in city A is _________.
Student/Subject
P
C
B
M
W
70
90
50
85
X
55
80
95
60
Y
60
20
90
40
Z
90
80
40
65
The given table represents the marks obtained by four students W, X, Y and Z in four subjects P, C, B and M, with the maximum marks in each subject being 100.
The average marks of the four students in P and C together (round to one decimal) is:
The average salary per year during period 2001 – 2006 is:
Based on the given data, the percentage of literates in City C is ______ (round to one decimal).
Based on the given data, the total number of candidates elected is _______.
Direction: Study the table given below and answer the following question.
City
Population
Literate
Illiterate
% of literates
A
200
150
50
-
B
-
200
100
66.6
C
150
50
100
-
D
120
-
90
25
Based on the given data, the total percentage of literates in the four cities together, round to one decimal, is ______.
The average expenditure per year during the period 2001-2006 is _____ (round off the nearest integer).
What is the total number of students in both, section A and B?
In which year did Bhutan’s rice production decrease for the first time?
Important Questions from Tabulation
Table shows income (in Rs.) received by 4 employees of a company during the month of December 2020 and all their income sources.
Source
Amit
Suresh
Nitin
Varun
Salary
35000
38000
29000
42000
Arrears
6000
6300
5000
7500
Bonus
1000
1100
1000
1240
Overtime
1800
1950
1400
1500
By what percent are the Arrears of Amit and Suresh taken together less than the Arrears of Nitin and Varun taken together?The table given below shows the GDP of two countries in different five years.
Country Years A B Y1 175 285 Y2 200 300 Y3 150 125 Y4 75 85 Y5 50 95 K1 = The value of average GDP of country A in all the 5 years.
K2 = The value of average GDP of country B in all the 5 years.
What is the value of (K1 + K2)?
Study the Table Properly and answer by interpreting the data
The table shows the percentage population of five districts in a state below poverty line and the proportion of males and females.
District Percentage of population
below poverty levelProportion of Male and Female Below poverty line (M:F) Above poverty Line (M:F) D1 15 2 : 3 3 : 2 D2 18 3 : 4 7 : 5 D3 20 2 : 5 3 : 4 D4 25 5 : 2 4 : 3 D5 12 3 : 7 2 : 7 If the total population in the district D3 is 40,000, then what is the population of below poverty line in the district D3, ?
The table given below shows the marks obtained by 4 students in 5 subjects. The maximum marks of each subject is 100.
Subjects
Students
P1
P2
P3
P4
S1
89
100
92
91
S2
62
52
72
37
S3
57
55
70
65
S4
76
85
76
58
S5
85
70
66
62
What is the total percent marks of P4?
The data given below shows the number of people who have saved a certain amount of money.
Savings
(in Rs.)
Number of people
5
1
15
3
20
4
25
2
30
1
35
1
40
2
What is the mode of the given data?
