The local office of the APP-CAB company evaluates the performance of five cab drivers,
Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in
five different parameters (P1 to P5) as given below:

P1: timely arrival

P2: behaviour

P3: comfortable ride

P4: driver’s familiarity with the route

P5: value for money

Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts – a fixed payment and final rating-based bonus. If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters. The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:

The following additional facts are known.

**Q.1 If Damodaran does not get a bonus, what is the maximum possible value of his final
rating?**
**Answer: 3**

**Q.2 If Eman gets a bonus, what is the minimum possible value of his final rating?**
**Answer: 1**

**Q.3 If all five drivers get bonus, what is the minimum possible value of the monthly
payment (in rupees) that a driver gets?**
**Answer: 3**

**Q.4 If all five drivers get bonus, what is the maximum possible value of the monthly
payment (in rupees) that a driver gets?
**
**Answer: 3**

**Solutions:**

**Q.1 **If Damodaran does not get a bonus , it means he must get at least 1 rating in one parameter .

Now he has rating 3 in P2. So in rest 4 parameter he should get rating 1 in one parameter and to maximize his overall rating he must get 5 rating in 2 other parameters and 4 in the rest parameters.

So maximum possible rating = (3+5+5+4+1)/5 = 18/5 = 3.6

**Q.2** As Eman has got rating 2 in P5. He gets bonus so he should get at least one 5 rating . Also he shouldn’t get ration 1 in any parameters.

Now as no one gets same rating in three parameters, to minimize Eman’s rating , he should get rating 2 in 2 parameters and rating 3 in other 2 parameters .

Final Rating = (2+2+3+3+5)/5 = 15/5 = 3.0

Correct Option 1) 3.0

** Q.3** To minimize the monthly payment , we need to minimize the final rating as we did in question 2.

As everyone is getting bonus , so no one will get rating 1 in any parameter.

Also Arun and Barun has got rating 5 in exactly one parameters and Chandan has got rating 5 in exactly two parameters.

Minimum possible final rating of Arun = (5+4+2+2+3)/5 =16/2 = 3.2

Salary of Arun = 1000 + 250*3.2 = Rs 1800

Minimum possible final rating of Barun = (5+3+2+2+3)/5 = 15/5 = 3.0

Salary of Barun = 1200+200*3.0 = Rs 1800

Minimum possible final rating of Chandan = (5+5+2+2+3)/5 = 17/5 = 3.4

Salary of Chandan = 1400 + 100*3.4 = 1740

Minimum possible final rating of Damodaran = (5+3+2+2+3)/5 = 15/5 = 3

Salary of Damodaran = 1300 + 150*3 = Rs 1750

Minimum possible final rating of Eman = (5+3+2+2+3)/5 = 15/5 = 3

Salary of Eman =1100 + 200*3 = Rs 1700

So minimum possible salary = 1700

Correct option 2) 1700

**Q.4** This question is similar to previous question , in this question we have to maximize the final rating for maximum possible salary . Taking those points in mind given in point 1 and point 2.

As everyone is getting bonus , so no one will get rating 1 in any parameter.

Also Arun and Barun has got rating 5 in exactly one parameters and Chandan has got rating 5 in exactly two parameters.

Maximum possible final rating of Arun = (5+4+4+3+3)/5 =19/2 = 3.8

Salary of Arun = 1000 + 250*3.8 = Rs 1950

Maximum possible final rating of Barun = (5+3+4+4+3)/5 = 19/5 = 3.8

Salary of Barun = 1200+200*3.8 = Rs 1960

Maximum possible final rating of Chandan = (5+5+2+4+4)/5 = 20/5 = 4.0

Salary of Chandan = 1400 + 100*4.0 = 1800

Maximum possible final rating of Damodaran = (5+3+4+4+5)/5 = 21/5 = 4.2

Salary of Damodaran = 1300 + 150*4.2 = Rs 1930

Maximum possible final rating of Eman = (5+2+5+4+4)/5 = 20/5 = 4.0

Salary of Eman =1100 + 200*4 = Rs 1900

So Maximum possible salary = 1960

Correct option 1) 1960

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P1: timely arrival

P2: behaviour

P3: comfortable ride

P4: driver’s familiarity with the route

P5: value for money

Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts – a fixed payment and final rating-based bonus. If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters. The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:

The following additional facts are known.

- Arun and Barun have got a rating of 5 in exactly one of the parameters. Chandan has got a rating of 5 in exactly two parameters.
- None of drivers has got the same rating in three parameters.

- 3.2
- 3.4
- 3.6
- 3.8

- 3.0
- 2.8
- 3.4
- 3.2

- 1740
- 1750
- 1700
- 1600

- 2050
- 1950
- 1960
- 1900

Now he has rating 3 in P2. So in rest 4 parameter he should get rating 1 in one parameter and to maximize his overall rating he must get 5 rating in 2 other parameters and 4 in the rest parameters.

So maximum possible rating = (3+5+5+4+1)/5 = 18/5 = 3.6

Now as no one gets same rating in three parameters, to minimize Eman’s rating , he should get rating 2 in 2 parameters and rating 3 in other 2 parameters .

Final Rating = (2+2+3+3+5)/5 = 15/5 = 3.0

Correct Option 1) 3.0

As everyone is getting bonus , so no one will get rating 1 in any parameter.

Also Arun and Barun has got rating 5 in exactly one parameters and Chandan has got rating 5 in exactly two parameters.

Minimum possible final rating of Arun = (5+4+2+2+3)/5 =16/2 = 3.2

Salary of Arun = 1000 + 250*3.2 = Rs 1800

Minimum possible final rating of Barun = (5+3+2+2+3)/5 = 15/5 = 3.0

Salary of Barun = 1200+200*3.0 = Rs 1800

Minimum possible final rating of Chandan = (5+5+2+2+3)/5 = 17/5 = 3.4

Salary of Chandan = 1400 + 100*3.4 = 1740

Minimum possible final rating of Damodaran = (5+3+2+2+3)/5 = 15/5 = 3

Salary of Damodaran = 1300 + 150*3 = Rs 1750

Minimum possible final rating of Eman = (5+3+2+2+3)/5 = 15/5 = 3

Salary of Eman =1100 + 200*3 = Rs 1700

So minimum possible salary = 1700

Correct option 2) 1700

As everyone is getting bonus , so no one will get rating 1 in any parameter.

Also Arun and Barun has got rating 5 in exactly one parameters and Chandan has got rating 5 in exactly two parameters.

Maximum possible final rating of Arun = (5+4+4+3+3)/5 =19/2 = 3.8

Salary of Arun = 1000 + 250*3.8 = Rs 1950

Maximum possible final rating of Barun = (5+3+4+4+3)/5 = 19/5 = 3.8

Salary of Barun = 1200+200*3.8 = Rs 1960

Maximum possible final rating of Chandan = (5+5+2+4+4)/5 = 20/5 = 4.0

Salary of Chandan = 1400 + 100*4.0 = 1800

Maximum possible final rating of Damodaran = (5+3+4+4+5)/5 = 21/5 = 4.2

Salary of Damodaran = 1300 + 150*4.2 = Rs 1930

Maximum possible final rating of Eman = (5+2+5+4+4)/5 = 20/5 = 4.0

Salary of Eman =1100 + 200*4 = Rs 1900

So Maximum possible salary = 1960

Correct option 1) 1960

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