XAT 2021 Question 13

Instructions

Read the following scenario and answer the three questions that follow.

A company awards incentives to its employees for successful project performances. It rates successful project performance in categories A*, A, B, and C. Employees, in solo projects rated A*, A, B, and C, are awarded incentives ₹6 lakh, ₹5 lakh, ₹3 lakh, and ₹1 lakh respectively. When a project has multiple team members, the following scheme is used to award the incentives:

For example, for a project rated A, with three members, the team lead gets ₹4 lakh, and the other team members get ₹2.5 lakh each. A project always has a single team lead.

Six employees: Altaf, Bose, Chakrabarthi, Dipa, Ernie, and Fatima receive a total of ₹45 lakh in incentives by participating in a total of eight different projects that does not involve any other person. Not all six employees are involved in all eight projects.

The following are additionally known about these eight projects:
1. One project involves all six employees. Four projects involve three each, and the rest, two each.
2. Exactly three projects are rated C, for which a total of ₹4.8 lakh is paid.
3. Only one project is rated A*.

Question 13

What BEST is known about the team composition for the project rated A*?

Solution

Total percentage incentive when number of team members = 1 = 100%

Total percentage incentive when the number of team members =2 =160%

Total percentage incentive when the number of team members =3=180%

Total percentage incentive when the number of team members =4= 190%

Total percentage incentive when the number of team members >4 = 200%

From 1, Number of people in 8 different projects = 6, 3, 3,3,3, 2,2,2 respectively

From 2, Given, exactly three projects are rated C and 4.8 lakh is paid in total

A minimum of 3 lakhs has to be paid for rating C => 3 *1.6 = 4.8lakhs => All 2 member teams have been rated C

From 3, one project has been rated A*. Let that project be handled by the team of 3 members => Incentives = 180% of 6 = 10.8 lakh

Now remaining 6,3,3,3 should be either rated A or B and the total incentives should be equal to 45 - 10.8-4.8 = 29.4 lakhs

Let us assume 6 has been rated B => Incentives = 200% of 3 = 6 lakhs

The remaining 23.4 lakhs should come from 180%. $$\frac{23.4}{1.8}=13\ lakhs$$

Hence the remaining 3,3,3 can be rated as A, A, B

Hence final ratings are and total payouts are

6 - B - 6lakhs

3- A - 9 lakhs

3-A - 9 lakhs

3-B - 5.4 lakhs

3-A* - 10.8lakhs

2-C - 1.6 lakhs

2-C - 1.6 lakhs

2-C - 1.6 lakhs


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