CAT 2020 Slot 3 DILR Question & Solution
Data Set
XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a penalty for non-delivery. The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date, the second gives the cumulative number of orders that were booked up to and including that day. The third column represents the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and including that day. It is known that the numbers of orders that were booked on the 11th, 12th, and 13th of the last month that took two days to deliver were 4, 6, and 8 respectively
Question 1
Among the following days, the largest fraction of orders booked on which day was lost?
Solution:
The cumulative orders booked by 19th are 337 and that of 18th are 332=> No. orders booked on 19th are 5
Similarly we can find the orders booked on that day till 14th.
Number of orders lost that were booked on 12th = Cumulative orders lost till 14th-Cumulative orders lost till 13th =92-91=1
Similarly, the number of orders lost till 17th can be found out.
Number of orders delivered on 13th are 11 out of which 4 are orders which were booked in 11th so, 7 must be the orders which were booked on 12th.
Similarly, we can find the orders which took 1day and 2 days to get delivered till 17th.
Now, total number of orders booked on 12th will be 7+6=1=14.
Fraction of orders booked on 15th that were lost = 12/28
Fraction of orders booked on 16th that were lost = 2/25
Fraction of orders booked on 13th that were lost =2/31
Fraction of orders booked on 14th that were lost = 12/30.
.'. Option A is correct answer.
Question 2
On which of the following days was the number of orders booked the highest?
Solution:
The cumulative orders booked by 19th are 337 and that of 18th are 332=> No. orders booked on 19th are 5
Similarly we can find the orders booked on that day till 14th.
Number of orders lost that were booked on 12th = Cumulative orders lost till 14th-Cumulative orders lost till 13th =92-91=1
Similarly, the number of orders lost till 17th can be found out.
Number of orders delivered on 13th are 11 out of which 4 are orders which were booked in 11th so, 7 must be the orders which were booked on 12th.
Similarly, we can find the orders which took 1day and 2 days to get delivered till 17th.
Now, total number of orders booked on 12th will be 7+6=1=14.
The total number of orders placed on 13th = 21+8+2 = 31
FRom the table we can determine that among options, number of orders booked on 13th are maximum.
Question 3
The delivery ratio for a given day is defined as the ratio of the number of orders booked on that day which are delivered on the next day to the number of orders booked on that day which are delivered on the second day after booking. On which of the following days, was the delivery ratio the highest?
Solution:
The cumulative orders booked by 19th are 337 and that of 18th are 332=> No. orders booked on 19th are 5
Similarly we can find the orders booked on that day till 14th.
Number of orders lost that were booked on 12th = Cumulative orders lost till 14th-Cumulative orders lost till 13th =92-91=1
Similarly, the number of orders lost till 17th can be found out.
Number of orders delivered on 13th are 11 out of which 4 are orders which were booked in 11th so, 7 must be the orders which were booked on 12th.
Similarly, we can find the orders which took 1day and 2 days to get delivered till 17th.
Now, total number of orders booked on 12th will be 7+6=1=14.
From the table we can determine that among options, number of orders booked on 13th are maximum.
For 15 the delivery ratio = 8/8 = 1
For 16 the delivery ratio = 13/10 = 1.3
For 13 the delivery ratio = 21/8 = 2.625
For 14 the delivery ratio = 15/3 = 5
Hence Option D
Question 4
The average time taken to deliver orders booked on a particular day is computed as follows. Let the number of orders delivered the next day be x and the number of orders delivered the day after be y. Then the average time to deliver order is $\frac{(x+2y)}{(x+y)}$. On which of the following days was the average time taken to deliver orders booked the least?
Solution:
The cumulative orders booked by 19th are 337 and that of 18th are 332=> No. orders booked on 19th are 5
Similarly we can find the orders booked on that day till 14th.
Number of orders lost that were booked on 12th = Cumulative orders lost till 14th-Cumulative orders lost till 13th =92-91=1
Similarly, the number of orders lost till 17th can be found out.
Number of orders delivered on 13th are 11 out of which 4 are orders which were booked in 11th so, 7 must be the orders which were booked on 12th.
Similarly, we can find the orders which took 1day and 2 days to get delivered till 17th.
Now, total number of orders booked on 12th will be 7+6=1=14.
FRom the table we can determine that among options, number of orders booked on 13th are maximum.
Average time can be calculated as follows
14 is the least