Question

Which of the following statements is/are true?
I: The total project-month was the same for the four employees.
II: The total employee-month was the same for the five projects.

• A. Only I
• B. Both I and II
• C. Only II
• D. Neither I nor II
• A. All four of them
• B. Only Tinni
• C. Only Abani and Bahni
• D. Only Abani, Bahni and Danni
• A. Project 3, Project 5
• B. Project 4, Project 5
• C. Project 1, Project 5
• D. Project 3, Project 4
• A. Danni, Tinni, Bahni, Abani
• B. Danni, Tinni, Abani, Bahni
• C. Bahni, Abani, Tinni, Danni
• D. Tinni, Danni, Abani, Bahni

Answer 1

The Correct Option is A

To determine which statement(s) is/are true, we must analyze the given schedule and definitions provided. We need to calculate the total project-month for the four employees and the total employee-month for the five projects.

Step-by-step Analysis:

I. Total project-month for the four employees:

• Calculate the number of months each employee worked across all projects:
  • Abani: Worked from January to March, March to May, July to September, totaling 8 months.
  • Bahni: Worked from March to May, May to July, September to December, totaling 8 months.
  • Danni: Worked from January to March, May to July, July to September, totaling 8 months.
  • Tinni: Worked from March to May, July to September, October to December, totaling 8 months.
• Each employee worked for 8 months in total, so the total project-month is the same for each employee.

II. Total employee-month for the five projects:

• Calculate the sum of months four employees worked on each project:
  • Project 1: January to March, 2 employees, total 6 months.
  • Project 2: March to May, 3 employees, total 9 months.
  • Project 3: May to July, 2 employees, total 6 months.
  • Project 4: July to September, 3 employees, total 9 months.
  • Project 5: September to December, 1 employee, total 3 months.
• The total employee-month is not the same for each project, with 6, 9, 6, 9, and 3 months respectively.

Conclusion

Based on the calculations, statement I is true, and statement II is false.

Thus, the correct answer is: Only I

Answer 2

To determine which employees did not work in multiple projects for any of the months in 2020, we analyze their respective project involvements based on the figure.

• Abani: Abani worked on two separate projects but never in the same month for more than one project. Therefore, Abani did not work across multiple projects in any given month.
• Bahni: Bahni similarly contributed to different projects in different months, ensuring no overlap in her monthly schedule.
• Danni: Danni also maintained distinct project involvement for each month, never working on multiple projects in a single month.
• Tinni: Upon inspection, Tinni engaged in overlapping projects during certain months, thus disqualifying her from not having worked in multiple projects in a single month.

Conclusively, the employees not involved in multiple projects in any month are Abani, Bahni, and Danni.

Answer 3

The problem requires us to determine which of the given pairs of projects had the same duration, measured in terms of the number of months during which at least one employee worked on the project. Referring to the provided schedule:

• Project 1: Check the duration by observing the months each employee worked. Combine the start and end months for Project 1.
• Project 3: Determine the earliest start month and the latest end month across employees working on Project 3.
• Project 4: Find the duration by analyzing employees' work months for Project 4.
• Project 5: Analyze when each employee starts and finishes for Project 5.

Using these steps reveals:

• Project 3: Start - January, End - April (4 months)
• Project 4: Start - February, End - May (4 months)

On comparing the options, both Project 3 and Project 4 have the same duration. Therefore, the correct pair is Project 3, Project 4.

Answer 4

To determine the list of employees in decreasing order of annual completion index, we need to calculate each employee's weighted average completion percentage. The weights are the number of months worked on their projects. Here is the step-by-step breakdown for each employee based on the given schedule:

Employee	Projects	Months	Completion
Abani	P1, P2, P3	3, 3, 2	60, 70, 80
Bahni	P1, P4	4, 2	30, 90
Danni	P2, P3, P5	2, 3, 1	90, 60, 80
Tinni	P4, P5	3, 3	80, 70

Calculating Annual Completion Index:

• For Abani: \[ \frac{(3 \times 60 + 3 \times 70 + 2 \times 80)}{(3 + 3 + 2)} = 67.5 \]
• For Bahni: \[ \frac{(4 \times 30 + 2 \times 90)}{(4 + 2)} = 50 \]
• For Danni: \[ \frac{(2 \times 90 + 3 \times 60 + 1 \times 80)}{(2 + 3 + 1)} = 70 \]
• For Tinni: \[ \frac{(3 \times 80 + 3 \times 70)}{(3 + 3)} = 75 \]

Final Ranking in Decreasing Order of Annual Completion Index:

Arranging them in decreasing order of annual completion index, we get:

Danni, Tinni, Abani, Bahni