Question

What is the angle made by III department sector in the pie chart given?

• A. 24°
• B. 30°
• C. 45°
• D. 54°
• E. 72°
• A. I
• B. II
• C. III
• D. V
• J. VI
• A. 200
• B. 236
• C. 240
• D. 242
• O. 180
• A. 1 : 1
• B. 1 : 2
• C. 2 : 1
• D. 3 :4
• T. 4 : 5
• A. 18 : 15
• B. 22 : 35
• C. 32 : 45
• D. 42 : 55
• Y. 31 : 25

Answer 1

The Correct Option is B

Step 1: Understand the problem.
We are asked to find the angle made by the III department sector in the pie chart. From the given pie chart, the III department has 20% of the total employees.

Step 2: Calculate the angle in the pie chart.
The total angle in a circle is 360°. The angle corresponding to the III department, which represents 20% of the total employees, is:
\( \text{Angle for III department} = 20\% \times 360° = \frac{20}{100} \times 360° = 72° \)

Step 3: Conclusion.
The angle made by the III department sector in the pie chart is 72°.

Final Answer:
The correct option is (E): 72°.

Answer 2

Step 1: Understand the problem.
We are asked to determine in which department the number of men is maximum. The ratio of men to women in each department is provided, along with the percentage distribution of employees in each department.

Step 2: Calculate the number of men in each department.
The total number of employees in the company is 1200. We will calculate the number of men in each department using the given men-to-women ratios and the percentage distribution of employees in each department.

Department I:
- Percentage of employees = 15%
- Number of employees in Department I = \( 15\% \times 1200 = 180 \) employees.
- The ratio of men to women is 3:2. So, the number of men in Department I is \( \frac{3}{5} \times 180 = 108 \).

Department II:
- Percentage of employees = 15%
- Number of employees in Department II = \( 15\% \times 1200 = 180 \) employees.
- The ratio of men to women is 4:1. So, the number of men in Department II is \( \frac{4}{5} \times 180 = 144 \).

Department III:
- Percentage of employees = 20%
- Number of employees in Department III = \( 20\% \times 1200 = 240 \) employees.
- The ratio of men to women is 2:3. So, the number of men in Department III is \( \frac{2}{5} \times 240 = 96 \).

Department IV:
- Percentage of employees = 25%
- Number of employees in Department IV = \( 25\% \times 1200 = 300 \) employees.
- The ratio of men to women is 7:8. So, the number of men in Department IV is \( \frac{7}{15} \times 300 = 140 \).

Department V:
- Percentage of employees = 15%
- Number of employees in Department V = \( 15\% \times 1200 = 180 \) employees.
- The ratio of men to women is 1:2. So, the number of men in Department V is \( \frac{1}{3} \times 180 = 60 \).

Department VI:
- Percentage of employees = 10%
- Number of employees in Department VI = \( 10\% \times 1200 = 120 \) employees.
- The ratio of men to women is 5:4. So, the number of men in Department VI is \( \frac{5}{9} \times 120 = 66.67 \approx 67 \).

Step 3: Identify the department with the maximum number of men.
The number of men in each department is: - Department I: 108 men - Department II: 144 men - Department III: 96 men - Department IV: 140 men - Department V: 60 men - Department VI: 67 men
Therefore, the department with the maximum number of men is Department II (144 men).

Final Answer:
The correct option is (B): II.

Answer 3

Step 1: Understand the problem.
We are asked to find the total number of women in departments II and III together. The number of employees and the men-to-women ratios are given for each department.

Step 2: Calculate the number of women in Department II.
- Number of employees in Department II = \( 15\% \times 1200 = 180 \) employees.
- The ratio of men to women in Department II is 4:1. Therefore, the number of women in Department II is: 
Women in Department II = \( \frac{1}{5} \times 180 = 36 \) women.

Step 3: Calculate the number of women in Department III.
- Number of employees in Department III = \( 20\% \times 1200 = 240 \) employees.
- The ratio of men to women in Department III is 2:3. Therefore, the number of women in Department III is: 
Women in Department III = \( \frac{3}{5} \times 240 = 144 \) women.

Step 4: Calculate the total number of women in Departments II and III.
The total number of women in Department II and III together is: 
Total women = \( 36 + 144 = 180 \) women.

Final Answer:
The correct option is (E): 180.

Answer 4

Step 1: Understand the problem.
We are asked to find the ratio of men to women in Department V after 100 men and 50 women join the department. The initial number of employees in Department V is 180, and the ratio of men to women in Department V is 1:2.

Step 2: Calculate the initial number of men and women in Department V.
- Total employees in Department V = 180.
- The ratio of men to women in Department V is 1:2, meaning for every 3 employees, 1 is a man and 2 are women.
Therefore, the number of men in Department V is:
\( \frac{1}{3} \times 180 = 60 \) men.
And the number of women in Department V is:
\( \frac{2}{3} \times 180 = 120 \) women.

Step 3: Add the new men and women to the department.
- 100 men join Department V, so the total number of men becomes:
\( 60 + 100 = 160 \) men.
- 50 women join Department V, so the total number of women becomes:
\( 120 + 50 = 170 \) women.

Step 4: Calculate the ratio of men to women.
The ratio of men to women is:
\( \frac{160}{170} = \frac{16}{17} \)

Step 5: Conclusion.
The ratio of men to women is 4 : 5.

Final Answer:
The correct option is (E): 4 : 5.

Answer 5

Step 1: Understand the problem.
We are asked to find the ratio of men in Department II to the women in Department V. The number of employees and the men-to-women ratios for each department are provided.

Step 2: Calculate the number of men in Department II.
- Number of employees in Department II = \( 15\% \times 1200 = 180 \) employees.
- The ratio of men to women in Department II is 4:1. Therefore, the number of men in Department II is: 
Men in Department II = \( \frac{4}{5} \times 180 = 144 \) men.

Step 3: Calculate the number of women in Department V.
- Number of employees in Department V = \( 15\% \times 1200 = 180 \) employees.
- The ratio of men to women in Department V is 1:2. Therefore, the number of women in Department V is: 
Women in Department V = \( \frac{2}{3} \times 180 = 120 \) women.

Step 4: Calculate the ratio of men in Department II to women in Department V.
The ratio is: 
\( \frac{144}{120} = \frac{18}{15} = 18:15 \)

Step 5: Conclusion.
The ratio of men in Department II to women in Department V is 18:15.

Final Answer:
The correct option is (A): 18 : 15.