CAT 2025 Lesson : Numerical Reasoning - Case 10

Read the following and answer the questions that follow

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.



[CAT 2020 S3]

34) Among the following days, the largest fraction of orders booked on which day was lost?

(1) 13th
(2) 14th
(3) 16th
(4) 15th

35) On which of the following days was the number of orders booked the highest?

(1) 14th
(2) 13th
(3) 12th
(4) 15th

36) 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?

(1) 15th
(2) 13th
(3) 16th
(4) 14th

37) 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 (x+2y)/(x+y). On which of the following days was the average time taken to deliver orders booked the least?

(1) 16th
(2) 14th
(3) 13th
(4) 15th

Solution

34


From the table, The cumulative orders booked and the cumulative orders lost can be calculated for each day but orders delivered by that day has two elements in it. It comprises of orders booked from previous day and the day before.. Thus the table can be re-written as follows,



As said, The orders delivered has two elements in it. Let
Orders booked from previous day = T1
Orders booked from Two days early = T2
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.



From the above table,

Total orders booked on 13th = T1(14^th) + T2(15^th) + Orders lost on 15^th orders booked on 13th = 21 + 8 + 2 = 31

Total orders booked on 14^th = T1(15^th) + T2(16^th) + Orders lost on 16^th
30 = 15 + 3 + 12

Follow the same set of steps to fill the rest.

Total orders booked on 15^th = T1(16^th) + T2(17^th) + Orders lost on 17^th
28 = 8 + 8 +12

Total orders booked on 16th = T1(17^th) + T2(18^th) + Orders lost on 18^th
25 = 13 + 10 + 2

Total orders booked on 17^th = T1(18^th) + T2(19^th) + Orders lost on 19^th
25 = 3 + 13 + 9

Total orders booked on 13^th = T1(14^th) + T2(15^th) + Orders lost on 15^th
31 = 21 + 8 + 2

Total orders booked on 12^th = T1(13^th) + T2(14^th) + Orders lost on 14^th
14 = 7 + 6 + 1


Considering options,


On comparing the fractions,
$\dfrac{12}{28}$is the largest.

Hence, Day 15^th has the largest fraction of orders booked on which day was lost. Answer: (4) 15^th

35


On considering options,
Day 13^th has the largest number of orders booked.

Answer: (2) 13^th

36)


Delivery ratio = $\dfrac{Orders \ delivered \ on \ the \ next \ day}{Orders \ delivered \ on \ two \ days \ after}$

Find delivery ratios for the given options.
13^th = 21/8
14^th = 15/3
15^th = 8/8
16^th = 13/10

Day 14^th has the highest delivery ratio. Answer: (4) 14^th

37)
Average time taken = $\dfrac{x + 2y}{x + y}$

= $\dfrac{x + y}{x + y} + \dfrac{y}{x + y}$

= $1 + \dfrac{y}{x + y}$



The lowest average time taken to deliver the orders is on the day 14^th

Answer: (2) 14^th

Answer:
34) (4) 15th
35) (2) 13th
36) (4) 14th
37) (2) 14th