CAT 2021 Slot 3 DILR Question & Solution
Data Set
The figure above shows the schedule of four employees - Abani, Bahni, Danni, and Tinni - whom Dhoni supervised in 2020. Altogether there were five projects which started and concluded in 2020 in which they were involved. For each of these projects and for each employee, the starting day was at the beginning of a month and the concluding day was the end of a month, and these are indicated by the left and right end points of the corresponding horizontal bars. The number within each bar indicates the percentage of assigned work completed by the employee for that project, as assessed by Dhoni.
For each employee, his/her total project-month (in 2020) is the sum of the number of months (s)he worked across the five projects, while his/her annual completion index is the weightage average of the completion percentage assigned from the different projects, with the weights being the corresponding number of months (s)he worked in these projects. For each project, the total employee-month is the sum of the number of months four employees worked in this project, while its completion index is the weightage average of the completion percentage assigned for the employees who worked in this project, with the weights being the corresponding number of months they worked in this project.
Question 1
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.
Solution:
The total project month is the number of months Abani, Bahni, Danni, and Tinni individually worked for all the projects combined :
Abani - 2+2+5 = 9 months
Bahni - 2+4+3 = 9 months
Danni - 3+3+2+1 = 9 months
Tinni - 2+2+3+2 = 9 months.
The total employee month for all the five projects is the sum of the total employee-month is the sum of the number of months four employees worked in this project.
Project -1 = 2+2+2 = 6 months
Project -2 = 3+2 = 5 months
Project - 3 = 2+4+3 = 9 months.
Project - 4 = 5+2+3 = 10 months.
Project - 5 = 3+1+2 = 6 months.
Only statement 1 is true.
Question 2
Which employees did not work in multiple projects for any of the months in 2020?
Solution:
Abani, Banni, and Danni did not work on multiple projects simultaneously in a month
Tinni was the only person who worked on multiple projects which are project 4 and project 5 in the month of september.
Question 3
The project duration, measured in terms of the number of months, is the time during which at least one employee worked in the project. Which of the following pairs of the projects had the same duration?
Solution:
Considering the information provided :
For project 1 : 3 months.
Project - 2: 3 months.
Project - 3: 5 months.
Project - 4: 5 months.
Project - 5: 4 months.
Among the given options option D is true which is project 3, project 4.
Question 4
The list of employees in decreasing order of annual completion index is:
Solution:
The annual completion index for different people is :
The weightage average of the completion percentage assigned from the different projects, with the weights being the corresponding number of months (s)he worked in these projects.
For Abani :
$\frac{\left(\left(100\cdot2\right)+\left(100\cdot2\right)+\left(80\cdot5\right)\right)}{2+2+5}=\ \frac{800}{9}$
For Bahni :
$\frac{\left(\left(100\cdot2\right)+\left(75\cdot4\right)+\left(90\cdot3\right)\right)}{2+3+4}=\ \frac{770}{9}$
For Danni :
$\frac{\left(\left(90\cdot3\right)+\left(100\cdot3\right)+\left(100\cdot2\right)+\left(100\cdot1\right)\right)}{2+3+2+1}=\ \frac{870}{9}$
For Tinni :
$\frac{\left(\left(80\cdot2\right)+\left(100\cdot2\right)+\left(100\cdot3\right)+\left(100\cdot2\right)\right)}{2+2+3+2}=\ \frac{860}{9}$
The descending order for the four people is :
Danni, Tinni, Abani, Bahni.