CAT 2021 Slot 2 — DILR Question 5
Answer the next 6 questions based on the information given
Ravi works in an online food-delivery company. After each delivery, customers rate Ravi on each of four parameters – Behaviour, Packaging, Hygiene, and Timeliness, on a scale from 1 to 9. If the total of the four rating points is 25 or more, then Ravi gets a bonus of â¹20 for that delivery. Additionally, a customer may or may not give Ravi a tip. If the customer gives a tip, it
is either â¹30 or â¹50.
One day, Ravi made four deliveries - one to each of Atal, Bihari, Chirag and Deepak, and received a total of â¹120 in bonus and tips. He did not get both a bonus and a tip from the same customer.
The following additional facts are also known.
- In Timeliness, Ravi received a total of 21 points, and three of the customers gave him the same rating points in this parameter. Atal gave higher rating points than Bihari and Chirag in this parameter.
- Ravi received distinct rating points in Packaging from the four customers adding up to 29 points. Similarly, Ravi received distinct rating points in Hygiene from the four customers adding up to 26 points.
- Chirag gave the same rating points for Packaging and Hygiene.
- Among the four customers, Bihari gave the highest rating points in Packaging, and Chirag gave the highest rating points in Hygiene.
- Everyone rated Ravi between 5 and 7 in Behaviour. Unique maximum and minimum ratings in this parameter were given by Atal and Deepak respectively.
- If the customers are ranked based on ratings given by them in individual parameters, then Atal’s rank based on Packaging is the same as that based on Hygiene. This is also true for Deepak.
What was the minimum rating that Ravi received from any customer in any parameter?
Answer & solution
Answer: 5
Timeliness:
From (1): Ravi’s rating in Timeliness by 4 customers can be either (6, 5, 5, 5) or (9, 4, 4, 4) where Atal’s rating will be higher than the other 3 customers.
Packaging:
From (2): Ravi’s rating in Packaging by 4 customers will be (9, 8, 7, 5) in any order.
From (4): Bihari’s rating in Packaging will be 9.
Hygiene:
âââââââFrom (3 and 4): Chirag gave highest rating in hygiene which is same as his rating in packaging. Since Chirag can not give a rating of 9 in packaging (which is given by Bihari), highest rating Chirag can give in hygiene can be 8 or lower, which is same as the rating given by him in packaging.
From (2 and 3 and 4): Ravi’s rating in Hygiene by 4 customers is (8, 7, 6, 5).
∴ Ratings given by Chirag in packaging and hygiene is 8.
Behaviour:
From (5): Ravi’s rating in Behaviour given by Atal and Deepak is 7 and 5 respectively and rating given by Bihari and Chirag is 6.
We can make the following table from the information we have so far.
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From (6): If Atal and Deepak will have the same ranking in packaging and hygiene.
Since Bihari and Chirag are given the two best rating in packaging, Atal and Deepak will give the two least ratings in packaging and hygiene.
∴ Rating given by Bihari in hygiene is 7.
Hence, we have two cases
Case 1:
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Case 2:
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[Note: Ravi gets a bonus of Rs. 20 from a customer if the total of four rating points by that customer is 25 or more. Else Ravi may or may not get a tip amount of Rs. 30 or Rs. 50.]
Consider Case 1: It is not possible for Ravi to earn a total amount of Rs. 120. Hence we can reject case 1.
Consider Case 2: For Ravi to earn a total amount of Rs. 120, he should not receive bonus from Atal.
∴ Ravi gets a total rating of < 25 from Atal. This is possible when Atal gives a rating of 6 for Timeliness.
Also, a total of Rs. 120 will be possible when Atal or Deepak give Ravi a tip amount of Rs. 30 or Rs. 50 in any order.
∴ We get the final table as below.
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∴ Minimum rating received by Ravi in any parameter is 5.
i.e., by Deepak in Behaviour, by Atal in Packaging etc.
Hence, 5.