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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:

P1P2P3P4P5Fixed PaymentBonus
Arun4Rs. 1000Rs. 250 × Final Rating
Barun3Rs. 1200Rs. 200 × Final Rating
Chandan2Rs. 1400Rs. 100 × Final Rating
Damodaran3Rs. 1300Rs. 150 × Final Rating
Eman2Rs. 1100Rs. 200 × Final Rating

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.

If Eman gets a bonus, what is the minimum possible value of his final rating?

Solution

✅ Correct Option: 3
Slide 1/2

Understanding the set :

  1. There are five cab driver - Arun, Barun, Chandan, Damodaran, and Eman, evaluated on five parameters -

P1: timely arrival

P2: behaviour

P3: comfortable ride

P4: driver's familiarity with the route

P5: value for money

on a scale of 1 to 5.

  1. final rating of a driver is the average of his ratings in these five parameters
  1. Two parts of monthly payments - fixed payment and final rating-based bonus
  1. 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.

This is a maxima minima set:

In this set not much information is given to us to fill the entire table directly,

Therefore, in this set rather than trying to solve the set directly we will go ahead with the questions and solve the set according to them.

NameP1P2P3P4P5Final RatingFixed PaymentBonus Formula
Arun4Rs.1000Rs.250 × Final Rating
Barun3Rs.1200Rs.200 × Final Rating
Chandan2Rs.1400Rs.100 × Final Rating
Damodaran3Rs.1300Rs.150 × Final Rating
Eman2Rs.1100Rs.200 × Final Rating

Question says,

If Eman gets a bonus, what is the minimum possible value of his final rating

For Eman to get bonus,

  1. he should have 5 in atleast one parameter.

  2. he should not have "1" in any of the parameter.

Therefore, 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.

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