Question

If Damodaran does not get a bonus, what is the maximum possible value of his final rating?

• A. 3.8
• B. 3.4
• C. 3.6
• D. 3.2
• A. 3.0
• B. 3.2
• C. 2.8
• D. 3.4
• A. 1740
• B. 1600
• C. 1700
• D. 1750
• A. 1960
• B. 1950
• C. 1900
• D. 2050

Answer 1

The Correct Option is C

To determine the maximum possible final rating for Damodaran, given that he does not get a bonus, follow these steps:

1. The bonus condition states that to qualify for a bonus, a driver must have at least one parameter rated with 5 and no parameter rated with 1. Since Damodaran doesn't receive a bonus, either all his parameters are rated below 5, or at least one parameter is rated 1.
2. Assume Damodaran has no 1's (as having a 1 would greatly reduce the average). Therefore, Damodaran must lack a 5 in any parameter.
3. The ratings range from 2 to 4. To maximize his average, posit the following:
   • Damodaran has three parameters rated at 4 and two at 3, as we seek to maximize his average while staying below 5.
4. Calculate the average:
   Let the ratings be 4, 4, 4, 3, 3.
   Sum = 4 + 4 + 4 + 3 + 3 = 18.
   Average = 18/5 = 3.6.
5. Thus, if Damodaran doesn't get a bonus, the maximum possible value of his final rating is 3.6.

Answer 2

To determine the minimum possible value of Eman's final rating, we need to consider the constraints and given data about the rating parameters. Here's the step-by-step breakdown:

1. Eman is only eligible for a bonus if he has a rating of 5 in at least one parameter and no rating of 1 in any parameter.
2. From the table, we see Eman's P5 rating is 2, removing one possible position for a rating of 5.
3. Assuming Eman has a rating of 5 in one of the remaining parameters (P1, P2, P3, or P4), let’s assume it's P1 for simplicity. Then, ratings must avoid any 1.
4. The objective is to minimize the average. Consider P2, P3 having ratings of 2, which maintains the constraint and allows the average to be low.
5. Assign a potential rating set for Eman:

   • P1=5 (Assume Eman scores highest here for bonus eligibility)
   • P2=2
   • P3=2
   • P4=3
   • P5=2
6. Calculate the final rating average:
   (5+2+2+3+2)/5=14/5=2.8
7. Since alternate configurations hold this threshold and cannot lower without affecting bonus eligibility, the solution alters:

8. Review possible ratings options: Assigning a modified set where the next addition increases slightly while honoring constraints.

   • P1=5
   • P2=3
   • P3=3
   • P4=2
   • P5=2
9. Recalculate the average: (5+3+3+2+2)/5=15/5=3.0

Therefore, the minimum possible final rating for Eman, given the constraint of bonus eligibility, is 3.0.

Answer 3

Driver	Parameter	P1	P2	P3	P4	P5	Fixed Payment	Bonus Multiplier
Arun	Rating	x1	x2	x3	4	5	1000	250
Barun	Rating	3	5	y3	y4	y5	1200	200
Chandan	Rating	z1	z2	2	5	5	1400	100
Damodaran	Rating	w1	3	w3	w4	5	1300	150
Eman	Rating	v1	v2	1	v4	2	1100	200

To determine the minimum possible monthly payment that a driver, who receives a bonus, could get, consider the driver with the lowest fixed payment and modify the ratings such that the average rating results in the minimum increment possible from bonus:

Analysis for Arun:

• Has a 5 in P5, ensuring eligibility for bonus.
• Minimized average rating occurs when:
  x1 + x2 + x3 + 4 + 5 = 15.
• Average rating: (x1 + x2 + x3 + 4 + 5)/5 = 3.
  Total: 15, so (x1 + x2 + x3) = 6
  Possible ratings: 2,2,2 .
• Final rating: 3
  Bonus: 3 × 250 = 750
• Total Payment: 1000 + 750 = 1750

Analysis for Barun:

• Has a 5 in P2, ensuring eligibility for bonus.
• Minimized average rating occurs when:
  3 + 5 + y3 + y4 + y5 = 15
• Average rating: (3 + 5 + y3 + y4 + y5)/5 = 3.
• To meet the rating sum = 15, choose: 2,2,3.
  So y3 = 2, y4 = 2, y5 = 3 .
• Final Rating: 3
  Bonus: 3 × 200 = 600
• Total Payment: 1200 + 600 = 1800

Analysis for Chandan:

• Has 5 in P4 and P5, ensuring eligibility for bonus.
• Average rating & minimization:
  z1 + z2 + 2 + 5 + 5 = 15
• Average rating: (z1 + z2 + 12)/5 = 3.
  So z1 + z2 = 3 => (1, 2)
• Final Rating: 3
  Bonus: 3 × 100 = 300
• Total Payment: 1400 + 300 = 1700

Analysis for Damodaran:

• Has a 5 in P5, ensuring eligibility for bonus.
• Rating sum scenario: w1 + 3 + w3 + w4 + 5 = 15
• Average: (w1 + 3 + w3 + w4 + 5)/5 = 3.
  So w1 + w3 + w4 = 7 => (2, 2, 3) .
• Final Rating: 3
  Bonus: 3 × 150 = 450
• Total Payment: 1300 + 450 = 1750

Analysis for Eman:

• Has a 1 in P3, not eligible for bonus.

The minimum possible value of the monthly payment for an eligible driver (after calculating all possible options) is 1700 (for Chandan).

Answer 4

To find the maximum monthly payment for a driver when all five receive a bonus, analyze each driver's ratings and payment structure.

1. **Arun: Total Fixed Payment Rs. 1000** 
- P4 rating = 4
- Bonus = 250 × Final Rating
- Needs a 5 in one parameter to qualify for bonus: P1, P2, P3, or P5 can be 5
- Remaining parameters should maximize the average, so assign: 5,5,4,5,4
- Final Rating = (5+5+4+5+4)/5 = 4.6
- Total Payment = Rs. 1000 + 250 × 4.6 = Rs. 2150
 

2. **Barun: Total Fixed Payment Rs. 1200**
- P1 rating = 3
- Bonus = 200 × Final Rating
- Needs a 5 in one parameter to qualify for bonus: P2, P3, P4, or P5 can be 5
- Remaining parameters should maximize the average, so assign: 3,5,4,5,5
- Final Rating = (3+5+4+5+5)/5 = 4.4
- Total Payment = Rs. 1200 + 200 × 4.4 = Rs. 2080
 

3. **Chandan: Total Fixed Payment Rs. 1400**
- P3 rating = 2
- Bonus = 100 × Final Rating
- Needs a 5 in two parameters: P1, P2, P4, or P5 can be 5
- Remaining parameters should maximize the average, so assign: 5,5,2,4,5
- Final Rating = (5+5+2+4+5)/5 = 4.2
- Total Payment = Rs. 1400 + 100 × 4.2 = Rs. 1842
 

4. **Damodaran: Total Fixed Payment Rs. 1300**
- P2 rating = 3
- Bonus = 150 × Final Rating
- Needs a 5 in one parameter to qualify for bonus: P1, P3, P4, or P5 can be 5
- Remaining parameters should maximize the average, so assign: 5,3,5,5,4
- Final Rating = (5+3+5+5+4)/5 = 4.4
- Total Payment = Rs. 1300 + 150 × 4.4 = Rs. 1960
 

5. **Eman: Total Fixed Payment Rs. 1100**
- P5 rating = 2
- Bonus = 200 × Final Rating
- Needs a 5 in one parameter to qualify for bonus: P1, P2, P3, or P4 can be 5
- Remaining parameters should maximize the average, so assign: 5,5,5,4,2
- Final Rating = (5+5+5+4+2)/5 = 4.2
- Total Payment = Rs. 1100 + 200 × 4.2 = Rs. 1840
 

Considering all calculations, the maximum monthly payment when all drivers receive a bonus is Rs. 1960. Hence, the correct answer is 1960.