CAT 2020 Slot 1 DILR Question & Solution
Data Set
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.
1. 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.
2. None of drivers has got the same rating in three parameters.
Question 1
If Damodaran does not get a bonus, what is the maximum possible value of his final rating?
Solution:
Based on the given conditions, Damodaran misses out on the bonus if he gets a rating of 1 in any of the five parameters. He additionally needs to obtain a rating of 5 in at least one of the parameters. Thus, the maximum value of the range of ratings that he can acquire would be 1+3(given)+5+5+5. However, based on condition 2, he can have similar ratings in only two of the parameters. Thus, the maximum value of the final rating would be (1+3+5+5+4) /5 = 18/5 = 3.6. Hence, Option C is the correct answer.
Question 2
If Eman gets a bonus, what is the minimum possible value of his final rating?
Solution:
Since Eman got a bonus, he must have obtained a rating of 5 in at least one of the parameters. To minimize his final rating we need to consider the following range of values: 5(mandatory)+2(given)+2+3+3 = 15. The least value of his final rating is, therefore, 15/5 = 3. Hence, Option D is the correct answer.
Question 3
If all five drivers get bonus, what is the minimum possible value of the monthly payment (in rupees) that a driver gets?
Solution:
Our objective here is to minimize the final ratings in order to find the minimum value of the monthly payment. We cannot have a rating of 1 in any of the parameters since all the drives got the bonus and we need to have at least one parameter with a rating of 5. With this understanding, we obtain the following:
Arun:
Final rating = (5+4+2+2+3)/5 = 16/5 = 3.2; Fixed payment = Rs.1000
Variable payment = 3.2 * Rs. 250 = Rs.800 ; Total = Rs.(1000+800) = Rs. 1800
Barun:
Final rating = (5+3+2+2+3)/5 = 15/5 = 3; Fixed payment = Rs.1200
Variable payment = 3 * Rs. 200 = Rs.600 ; Total = Rs.(1200+600) = Rs. 1800
Chandan: {rating of 5 in exactly two parameters based on condition 1}
Final rating = (5+5+2+2+3)/5 = 17/5 = 3.4; Fixed payment = Rs.1400
Variable payment = 3.4 * Rs. 100 = Rs.340 ; Total = Rs.(1400+340) = Rs. 1740
Damodaran:
Final rating = (5+3+2+2+3)/5 = 15/5 = 3; Fixed payment = Rs.1300
Variable payment = 3 * Rs. 150 = Rs.450 ; Total = Rs.(1300+450) = Rs. 1750
Eman:
Final rating = (5+3+2+2+3)/5 = 15/5 = 3; Fixed payment = Rs.1100
Variable payment = 3 * Rs. 200 = Rs.600 ; Total = Rs.(1100+600) = Rs. 1700
Hence, we observe that the minimum value of the monthly payment is Rs. 1700. Option D is the correct answer.
Question 4
If all five drivers get bonus, what is the maximum possible value of the monthly payment (in rupees) that a driver gets?
Solution:
Our objective here is to maximize the final ratings in order to find the maximum possible value of the monthly payment. We cannot have a rating of 1 in any of the parameters since all the drives got the bonus and we need to have at least one parameter with a rating of 5. With this understanding, we obtain the following:
Arun: {can have only one rating of 5 based on condition 1}
Final rating = (5+4+4+3+3)/5 = 19/5 = 3.8; Fixed payment = Rs.1000
Variable payment = 3.8 * Rs. 250 = Rs.950 ; Total = Rs.(1000+950) = Rs. 1950
Barun: {can have only one rating of 5 based on condition 1}
Final rating = (5+4+4+3+3)/5 = 19/5 = 3.8; Fixed payment = Rs.1200
Variable payment = 3.8 * Rs. 200 = Rs.760 ; Total = Rs.(1200+760) = Rs. 1960
Chandan:
Final rating = (5+5+2+4+4)/5 = 20/5 = 4; Fixed payment = Rs.1400
Variable payment = 4 * Rs. 100 = Rs.400 ; Total = Rs.(1400+400) = Rs. 1800
Damodaran:
Final rating = (5+5+4+4+3)/5 = 21/5 = 4.2; Fixed payment = Rs.1300
Variable payment = 4.2 * Rs. 150 = Rs.630 ; Total = Rs.(1300+630) = Rs. 1930
Eman:
Final rating = (5+5+2+4+4)/5 = 20/5 = 4; Fixed payment = Rs.1100
Variable payment = 4 * Rs. 200 = Rs.800 ; Total = Rs.(1100+800) = Rs. 1900
Hence, we observe that the maximum possible value of the monthly payment is Rs. 1960. Option A is the correct answer.