Read the following caselet and answer the questions based on the information provided.
In a college, there are a total of 2000 students across three streams: Science, Commerce, and Arts. The number of students in the Science stream is 900, and 30% of them are girls. The Commerce stream has 350 students, with a ratio of boys to girls being 3:4. The remaining students are in the Arts stream, where 40% of the students are boys.
What is the total number of students in the college?
Answer: C
The caselet states the total directly: the college has 2000 students, made up of 900 in Science, 350 in Commerce and the remaining 750 in Arts.
\[ 900 + 350 + 750 = 2000 \]
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What is the ratio of the number of boys to the number of girls in the college?
Answer: B
Correct answer: 27:23
Take the streams one at a time. Arts has \(2000 - 900 - 350 = 750\) students.
Science (900). 30% are girls, so girls \(= 270\) and boys \(= 630\).
Commerce (350). The ratio 3:4 makes 7 parts of 50, so boys \(= 150\) and girls \(= 200\).
Arts (750). 40% are boys, so boys \(= 300\) and girls \(= 450\).
\[\text{Boys} = 630 + 150 + 300 = 1080, \qquad \text{Girls} = 270 + 200 + 450 = 920\]
\[1080 : 920 = 27 : 23\]
The two totals add to 2000, which is the check that no stream has been missed.
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The number of girls in the Science stream is what percentage of the number of boys in the Arts stream?
Answer: A
First, we need to find the specific numbers from the caselet data.
Number of girls in Science = 30% of 900 = 0.30 * 900 = 270.
Number of boys in Arts = 60% of 750 = 0.60 * 750 = 450.
Required Percentage = \(\frac{\text{Girls in Science}}{\text{Boys in Arts}} \times 100\)
= \(\frac{270}{450} \times 100 = \frac{3}{5} \times 100 = 60\)%.
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The following data consists of a line graph showing the percentage of rural population in five different states and a table showing the total population of these states. Study the data and answer the questions.
Line Graph: Rural Population %
Table: Total Population
| State | Total Population (in millions) |
|---|---|
| A | 20 |
| B | 25 |
| C | 30 |
| D | 25 |
| E | 20 |
What is the total rural population of State A and State C together?
Answer: C
We need to calculate the rural population for each state and then add them.
State A: Total Population = 20 million. Rural Population % = 60%.
Rural Population = 60% of 20 million = 0.60 * 20 = 12 million.
State C: Total Population = 30 million. Rural Population % = 45%.
Rural Population = 45% of 30 million = 0.45 * 30 = 13.5 million.
Total Rural Population (A + C) = 12 + 13.5 = 25.5 million.
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The total urban population of State D is what percentage of the total population of State B?
Answer: B
First, find the urban population of State D.
Rural population % for State D = 55%. Therefore, Urban population % = 100% - 55% = 45%.
Total population of State D = 25 million.
Urban Population of D = 45% of 25 million = 0.45 * 25 = 11.25 million.
Total population of State B = 25 million.
Required Percentage = \(\frac{\text{Urban Pop. D}}{\text{Total Pop. B}} \times 100 = \frac{11.25}{25} \times 100 = 0.45 \times 100 = 45\)%.
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What is the ratio of the urban population of State E to the rural population of State A?
Answer: A
First, calculate the required populations.
Urban Population of State E:
Rural % = 40%, so Urban % = 60%.
Total Population = 20 million.
Urban Population = 60% of 20 million = 12 million.
Rural Population of State A:
Rural % = 60%.
Total Population = 20 million.
Rural Population = 60% of 20 million = 12 million.
The ratio is 12 million : 12 million, which simplifies to 1:1.
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The following data shows the distribution of employees in a company across different departments and the ratio of males to females in them. The total number of employees in the IT department is 990. Study the data and answer the questions.
Pie Chart: Employee Distribution by Department
Table: Male to Female Ratio
| Department | Male : Female Ratio |
|---|---|
| HR | 1:2 |
| Accounts | 4:5 |
| Production | 11:7 |
| IT | 5:4 |
| Marketing | 7:8 |
What is the total number of employees in the company?
Answer: D
The question provides the number of employees in the IT department, which can be used to find the total.
Number of employees in IT = 990.
From the pie chart, the percentage of employees in IT = 22%.
Let T be the total number of employees.
22% of T = 990
0.22 * T = 990
T = 990 / 0.22 = 4500.
The total number of employees is 4500.
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What is the total number of male employees in the company?
Answer: B
Correct answer: 2280
The IT department is 22% of the workforce and holds 990 people, so the company total is
\[\frac{990}{0.22} = 4500\]
Apply each department’s percentage, then split it by the male:female ratio.
HR, 12% of 4500 = 540, ratio 1:2, males \(= \tfrac{1}{3}\times 540 = 180\).
Accounts, 18% = 810, ratio 4:5, males \(= \tfrac{4}{9}\times 810 = 360\).
Production, 28% = 1260, ratio 11:7, males \(= \tfrac{11}{18}\times 1260 = 770\).
IT, 22% = 990, ratio 5:4, males \(= \tfrac{5}{9}\times 990 = 550\).
Marketing, 20% = 900, ratio 7:8, males \(= \tfrac{7}{15}\times 900 = 420\).
\[180 + 360 + 770 + 550 + 420 = 2280\]
The remaining 2220 employees are female, and the two figures add back to 4500.
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What is the ratio of the number of females in the Production department to the number of males in the Marketing department?
Answer: B
Correct answer: 7:6
The IT department is 22% of the workforce and holds 990 people, so the total is \(\tfrac{990}{0.22} = 4500\).
Females in Production. The department is 28% of 4500, or 1260, split 11:7 over 18 parts of 70:
\[\frac{7}{18} \times 1260 = 490\]
Males in Marketing. The department is 20% of 4500, or 900, split 7:8 over 15 parts of 60:
\[\frac{7}{15} \times 900 = 420\]
\[490 : 420 = 49 : 42 = 7 : 6\]
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What is the number of employees in the HR department?
Answer: A
From the first question under this direction, we found the total number of employees to be 4500.
The pie chart shows that 12% of employees are in the HR department.
Number of HR employees = 12% of 4500 = 0.12 * 4500 = 540.
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