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Company Project Incentives Analysis

XAT 2021 · Quantitative Ability & Data Interpretation · Hard · Data Interpretation

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Passage / data set

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:

No. of team-membersTeam lead getsOther members get
1100%-
290%70%
380%50% each
470%40% each
More than 4Every member gets (200/n)%(200/n)\%, where n=number of team membersn = \text{number of team members}

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 1 of 3

What BEST is known about the team compositions for the projects rated C?

  1. A.

    The three teams have two, three and six members respectively.

  2. B.

    All are either two-member or three-member teams.

  3. C.

    All are three-member teams.

  4. D.

    One is the six-member team, the rest are two-member teams.

  5. E.

    All are two-member teams.

Answer

E

Explanation

For a 2-member team, payout = 90%+70%=160%90\% + 70\% = 160\% of base. For C-rated project, base = ₹1 lakh. 160% of ₹1 lakh = ₹1.6 lakh. 3 such 2-member teams = 3×1.6=4.83 \times 1.6 = 4.8 lakh. Since total paid for C projects is ₹4.8 lakh, all three C-rated projects must be 2-member teams.

Question 2 of 3

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

  1. A.

    A three-member team

  2. B.

    Either a three-member team or the six-member team

  3. C.

    A two-member team

  4. D.

    Either a two-member team or a three-member team

  5. E.

    The six-member team

Answer

A

Explanation

All 2-member teams are C-rated. The remaining 5 projects consist of one 6-member team and four 3-member teams. Base for A* is 6 lakh. For 3-member team: payout = 180%×6=10.8180\% \times 6 = 10.8 lakh. For 6-member team: payout = 200%×6=12.0200\% \times 6 = 12.0 lakh. Solving payout constraints gives A* as a 3-member team.

Question 3 of 3

Total amount of money paid for projects rated A (in lakhs of Rupees) is:

  1. A.

    19

  2. B.

    15

  3. C.

    16

  4. D.

    17

  5. E.

    18

Answer

E

Explanation

The 8 projects are: 3 C-rated 2-member teams: 3×1.6=4.83 \times 1.6 = 4.8 lakh. 1 A*-rated 3-member team: 180%×6=10.8180\% \times 6 = 10.8 lakh. Remaining 4 projects: 6-member team (rated B, payout 200%×3=6200\% \times 3 = 6 lakh), two A-rated 3-member teams (2×180%×5=182 \times 180\% \times 5 = 18 lakh), and one B-rated 3-member team (180%×3=5.4180\% \times 3 = 5.4 lakh). Total = 4.8+10.8+6+18+5.4=454.8 + 10.8 + 6 + 18 + 5.4 = 45 lakh. Thus, money paid for projects rated A is 18 lakh.

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