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
What is the respective ratio of the number of boys in College‐C, the number of girls in College‐B and the total number of students in College‐E?
45 ∶ 7 ∶ 87
Understanding the College Student Distribution Data
The problem provides data about the distribution of students across six colleges (A-F) and the number of boys in each college. We are given the total number of students across all colleges, which is 12000. The table shows the percentage of the total students in each college and the absolute number of boys in each college.
The table is presented below:
| 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 |
We need to find the ratio of three specific values:
- The number of boys in College-C.
- The number of girls in College-B.
- The total number of students in College-E.
Calculating the Required Values from College Data
1. Number of Boys in College-C
This value is directly given in the table. Number of boys in College-C = 1800.
2. Number of Girls in College-B
To find the number of girls in College-B, we first need to calculate the total number of students in College-B. The table states that 9% of the total students are in College-B.
Total students in all colleges = 12000.
Total students in College-B = 9% of 12000
Total students in College-B = $\frac{9}{100} \times 12000$
Total students in College-B = $9 \times 120 = 1080$
The number of boys in College-B is given as 800.
Number of girls in College-B = Total students in College-B - Number of boys in College-B
Number of girls in College-B = $1080 - 800 = 280$
3. Total Number of Students in College-E
To find the total number of students in College-E, we use the percentage given in the table. The table states that 29% of the total students are in College-E.
Total students in all colleges = 12000.
Total students in College-E = 29% of 12000
Total students in College-E = $\frac{29}{100} \times 12000$
Total students in College-E = $29 \times 120$
Total students in College-E = $3480$
Determining the Ratio
Now we have the three required values:
- Number of boys in College-C = 1800
- Number of girls in College-B = 280
- Total number of students in College-E = 3480
The ratio is the number of boys in College-C : number of girls in College-B : total number of students in College-E.
Ratio = 1800 : 280 : 3480
To simplify the ratio, we need to find the greatest common divisor (GCD) of 1800, 280, and 3480. We can start by dividing by common factors.
Divide by 10:
1800 ÷ 10 = 180
280 ÷ 10 = 28
3480 ÷ 10 = 348
The ratio becomes 180 : 28 : 348.
Now, let's check for common factors of 180, 28, and 348. All are even numbers, so they are divisible by 2.
180 ÷ 2 = 90
28 ÷ 2 = 14
348 ÷ 2 = 174
The ratio becomes 90 : 14 : 174. All are still even.
Divide by 2 again:
90 ÷ 2 = 45
14 ÷ 2 = 7
174 ÷ 2 = 87
The ratio becomes 45 : 7 : 87.
Now, check if 45, 7, and 87 have any common factors other than 1. 45 = $3^2 \times 5$ 7 = 7 (prime number) 87 = $3 \times 29$ There are no common factors other than 1. So, the simplified ratio is 45 : 7 : 87.
Comparing this with the given options, we find that this ratio matches option 3.
Ratio Calculation Summary
- Boys in College C: 1800
- Girls in College B: 280
- Total Students in College E: 3480
- Initial Ratio: 1800 : 280 : 3480
- Simplified Ratio (divided by 40): 45 : 7 : 87
| Component | Value |
|---|---|
| Boys in College C | 1800 |
| Girls in College B | 280 |
| Total Students in College E | 3480 |
| Ratio (simplified) | 45 : 7 : 87 |
Revision Table: Key Data Points
| College | Total Students (calculated) | Number of Boys (given) | Number of Girls (calculated) |
|---|---|---|---|
| A | $12\% \text{ of } 12000 = 1440$ | 1000 | $1440 - 1000 = 440$ |
| B | $9\% \text{ of } 12000 = 1080$ | 800 | $1080 - 800 = 280$ |
| C | $26\% \text{ of } 12000 = 3120$ | 1800 | $3120 - 1800 = 1320$ |
| D | $18\% \text{ of } 12000 = 2160$ | 1200 | $2160 - 1200 = 960$ |
| E | $29\% \text{ of } 12000 = 3480$ | 2400 | $3480 - 2400 = 1080$ |
| F | $6\% \text{ of } 12000 = 720$ | 200 | $720 - 200 = 520$ |
Additional Information: Percentage Calculations and Ratios
This problem involves calculating values based on percentages and then finding a ratio. Understanding how to work with percentages and simplify ratios is key to solving data interpretation questions like this.
- Percentage Calculation: To find a percentage of a total number, you can convert the percentage to a decimal (divide by 100) and multiply by the total number, or use the formula: Value = $\frac{\text{Percentage}}{100} \times \text{Total}$.
- Ratio: A ratio is a comparison of two or more quantities. Ratios can be simplified by dividing all parts of the ratio by their greatest common divisor (GCD). Simplifying a ratio does not change its value, only its representation in the smallest possible whole numbers.
- Data Interpretation: Problems like this require carefully reading the given data, identifying what is being asked, and performing the necessary calculations step-by-step. Always double-check your calculations, especially when dealing with multiple steps.
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?
