The following table shows the percentage (%) distribution of students studying in six classes A-F of a school and shows the ratio of boys to girls among them. Number of students studying in all six classes together is 600. Class-wise distribution of students Ratio Boys ∶ Girls Class % Students A 20% 3 ∶ 2 B 12% 3 ∶ 1 C 16% 5 ∶ 3 D 15% 8 ∶ 7 E 21% 4 ∶ 3 F 16% 1 ∶ 1
Number of boys in class B is _________ % more than the number of girls in class F.
The question asks us to find the percentage by which the number of boys in class B is more than the number of girls in class F, based on the provided student distribution data and ratios.
Analyzing Student Distribution Data
We are given the percentage distribution of students across six classes (A to F) and the ratio of boys to girls in each class. The total number of students in the school is 600.
| Class | % Students | Ratio Boys : Girls |
|---|---|---|
| A | 20% | 3 : 2 |
| B | 12% | 3 : 1 |
| C | 16% | 5 : 3 |
| D | 15% | 8 : 7 |
| E | 21% | 4 : 3 |
| F | 16% | 1 : 1 |
Calculating Student Numbers by Class
First, we need to calculate the total number of students in Class B and Class F from the total school strength of 600.
- Total students in Class B = 12% of 600
- Total students in Class F = 16% of 600
Calculation for Class B:
Total students in Class B = $\frac{12}{100} \times 600 = 12 \times 6 = 72$ students.
Calculation for Class F:
Total students in Class F = $\frac{16}{100} \times 600 = 16 \times 6 = 96$ students.
Finding Boys in Class B and Girls in Class F
Next, we use the given boy-girl ratios for each class to find the specific numbers.
Number of Boys in Class B
The ratio of boys to girls in Class B is 3 : 1. The total number of parts in the ratio is $3 + 1 = 4$.
Number of boys in Class B = $\frac{\text{Number of boys parts}}{\text{Total ratio parts}} \times \text{Total students in Class B}$
Number of boys in Class B = $\frac{3}{4} \times 72 = 3 \times \frac{72}{4} = 3 \times 18 = 54$ boys.
Number of Girls in Class F
The ratio of boys to girls in Class F is 1 : 1. The total number of parts in the ratio is $1 + 1 = 2$.
Number of girls in Class F = $\frac{\text{Number of girls parts}}{\text{Total ratio parts}} \times \text{Total students in Class F}$
Number of girls in Class F = $\frac{1}{2} \times 96 = 48$ girls.
Calculating Percentage Increase
We need to find how much the number of boys in Class B (54) is more than the number of girls in Class F (48), expressed as a percentage of the number of girls in Class F.
Percentage increase = $\frac{(\text{Number of boys in B}) - (\text{Number of girls in F})}{\text{Number of girls in F}} \times 100\%$
Percentage increase = $\frac{54 - 48}{48} \times 100\%$
Percentage increase = $\frac{6}{48} \times 100\%$
Percentage increase = $\frac{1}{8} \times 100\%$
Percentage increase = $0.125 \times 100\% = 12.5\%$.
Thus, the number of boys in class B is 12.5% more than the number of girls in class F.
Revision Table: Key Concepts
| Concept | Description | Formula/Method |
|---|---|---|
| Percentage Calculation | Finding a part of a whole based on a percentage. | $\text{Part} = \frac{\text{Percentage}}{100} \times \text{Whole}$ |
| Ratio Division | Dividing a quantity into parts based on a given ratio. | $\text{Part} = \frac{\text{Ratio Part}}{\text{Sum of Ratio Parts}} \times \text{Total Quantity}$ |
| Percentage Increase | Calculating the relative increase of a value with respect to a base value. | $\text{Percentage Increase} = \frac{(\text{New Value} - \text{Old Value})}{\text{Old Value}} \times 100\%$ |
Additional Information on Data Analysis
This problem involves interpreting data presented in a table, performing percentage calculations, and applying ratio concepts. Data interpretation is a crucial skill in various quantitative aptitude tests. It often requires careful reading of tables or charts, extracting relevant information, and performing calculations based on percentages, ratios, averages, etc.
Understanding how to work with percentages and ratios is fundamental. A percentage represents a fraction out of 100. A ratio expresses the relative size of two or more values. When a quantity is divided in a given ratio, the total quantity is split into parts proportional to the ratio components.
Percentage increase or decrease is a common calculation to compare two values. The base value for the percentage calculation is critical; in this case, it's the number of girls in Class F because we are finding how much more the boys in Class B are *than* the girls in Class F.
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?
