Read the given passage and answer the questions that follow. The following table presents the details about the percentage (%) distribution of students and the number of boys in six different colleges (A‐F). There is a total of 12000 students in all the six colleges together. Based on the data in the table, answer the questions. College‐wise Distribution of Students College ↓ Percentage (%) of students Number of Boys A 12% 1000 B 9% 800 C 26% 1800 D 18% 1200 E 29% 2400 F 6% 200
In which of the following colleges is the total number of students equal to the number of girls in College‐E?
B
Solving College Student Distribution Problem
This problem requires us to analyze the provided data table showing the distribution of students across six different colleges (A-F) and the number of boys in each college. The total number of students across all colleges is given as 12000. We need to find which college has a total number of students equal to the number of girls in College E.
Understanding the Data Table
The table provides two key pieces of information for each college:
- Percentage (%) of total students
- Number of boys
The total number of students is 12000.
| College | Percentage (%) of students | Number of Boys |
|---|---|---|
| A | 12% | 1000 |
| B | 9% | 800 |
| C | 26% | 1800 |
| D | 18% | 1200 |
| E | 29% | 2400 |
| F | 6% | 200 |
Step-by-Step Calculation
Step 1: Calculate the total number of students in each college.
The total number of students is 12000. We can find the number of students in each college by using the given percentages.
- College A: $12\% \text{ of } 12000 = \frac{12}{100} \times 12000 = 0.12 \times 12000 = 1440$
- College B: $9\% \text{ of } 12000 = \frac{9}{100} \times 12000 = 0.09 \times 12000 = 1080$
- College C: $26\% \text{ of } 12000 = \frac{26}{100} \times 12000 = 0.26 \times 12000 = 3120$
- College D: $18\% \text{ of } 12000 = \frac{18}{100} \times 12000 = 0.18 \times 12000 = 2160$
- College E: $29\% \text{ of } 12000 = \frac{29}{100} \times 12000 = 0.29 \times 12000 = 3480$
- College F: $6\% \text{ of } 12000 = \frac{6}{100} \times 12000 = 0.06 \times 12000 = 720$
Step 2: Calculate the number of girls in College E.
The number of girls in any college is the total number of students in that college minus the number of boys in that college.
Number of Girls in College E = Total students in College E - Number of boys in College E
From Step 1, Total students in College E = 3480.
From the table, Number of boys in College E = 2400.
Number of Girls in College E = $3480 - 2400 = 1080$
Step 3: Find the college where the total number of students is equal to the number of girls in College E.
We need to check which college from Step 1 has a total number of students equal to 1080 (the number of girls in College E).
- Total students in College A = 1440
- Total students in College B = 1080
- Total students in College C = 3120
- Total students in College D = 2160
- Total students in College E = 3480
- Total students in College F = 720
Comparing the total number of students in each college with the number of girls in College E (1080), we find that the total number of students in College B is 1080.
Therefore, the total number of students in College B is equal to the number of girls in College E.
Summary of Student Counts
| College | Total Students | Number of Boys | Number of Girls |
|---|---|---|---|
| A | 1440 | 1000 | $1440 - 1000 = 440$ |
| B | 1080 | 800 | $1080 - 800 = 280$ |
| C | 3120 | 1800 | $3120 - 1800 = 1320$ |
| D | 2160 | 1200 | $2160 - 1200 = 960$ |
| E | 3480 | 2400 | $3480 - 2400 = 1080$ |
| F | 720 | 200 | $720 - 200 = 520$ |
The number of girls in College E is 1080. The college with a total of 1080 students is College B.
Conclusion
Based on the calculations, the total number of students in College B is equal to the number of girls in College E.
Revision Table: College Data Analysis
| Concept | Formula/Method | Application |
|---|---|---|
| Total Students per College | Total Students $\times$ Percentage / 100 | Used total 12000 students and college percentages |
| Number of Girls | Total Students - Number of Boys | Calculated for College E using its total students and boys |
| Comparison | Match value of Girls (College E) with Total Students (other colleges) | Matched 1080 (Girls in E) with Total Students in College B |
Additional Information: Percentage Calculations in Data Interpretation
Percentage calculations are fundamental in data interpretation problems. A percentage represents a part of a whole expressed as a fraction of 100. To find the value of a percentage of a total number, you can use the formula:
$\text{Value} = \frac{\text{Percentage}}{100} \times \text{Total Number}$
In this problem, we used this concept to find the number of students in each college from the total number of students (12000) and the given percentage distribution.
Also, understanding the relationship between total, parts (like boys and girls), is crucial:
$\text{Total} = \text{Part 1} + \text{Part 2}$
Here, Total Students = Number of Boys + Number of Girls. If you know any two, you can find the third.
Important Questions from Tabulation
The table shows District-wise data of a number of primary school teachers posted in schools of a city.
Study the table and answer the question:
District
Male teachers
Female teachers
East
1650
2375
North
1075
2651
West
1280
1520
South
1170
1085
Central
690
859
What is the difference between the total number of male teachers in the districts East, North, West taken together and the total number of female teachers in the districts East and South?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
38500
29000
42000
Arrears
6000
6300
5000
7500
Bonus
1000
1100
1000
1240
Overtime
1800
1950
1400
1500
What is the ratio of salary of Varun to his income other than salary?Study the table and answer the question:
Income (Rs.)
No. of persons
Less than 200
12
Less than 250
26
Less than 300
34
Less than 350
40
Less than 400
50
What is the percentage of persons earning Rs. 250 or more?The following table shows the annual profit of a company (in Rs. lakh).
2014-2015
2015-2016
2016-0217
2017-2018
2018-2019
625
690
725
775
815
The period which has the maximum percentage increase in profit over the previous year is:
The table given below shows the number of persons participating in a survey from 6 different states.
States Persons S1 100 S2 200 S3 400 S4 500 S5 600 S6 800 What is the ratio of number of person participating in a survey from state S3 to the number of person participating in a survey from state S4?
