Data Interpretation

Tables

Medium

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.

Day	Cumulative orders booked	Orders delivered on day	Cumulative orders lost
13th	219	11	91
14th	249	27	92
15th	277	23	94
16th	302	11	106
17th	327	21	118
18th	332	13	120
19th	337	14	129

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

13th

16th

15th

14th

✅ Correct Option: 3

Slide 1/9

Understanding the set :-

This set provides information about a delivery company that offers a 2-day delivery promise.

If an item is not delivered within 2 days, it is declared as "lost". In such cases, the payment is refunded along with a penalty.

In this set it is very important to understand that cumulative or total will be the total orders until that day.

[For eg - if order on day 1 - 2 ;day 2 - 4; day 3 - 3; day 4 - 5

=> cumulative on day 4 will be 2 + 4 + 3 + 5 = 14

similarly, cumulative on day 3 = 2 + 4 + 3 = 9

Therefore, to find orders on day 4 we can directly subtract cumulative of day 4 from day 3 = 14 - 9 = 5 ]

3)This is a Table + Data Interpretation (DI) set.

In this set, we need to determine the number of orders booked each day starting from the 11th, and also identify the number of items that were:

-Delivered the next day

-Delivered after two days

-Or lost

This is a very common type of set where you're given cumulative data and are required to calculate definite values from it.

Therefore, this set serves as a valuable learning opportunity.

Date	2-day Delivery	Delivery Done on the Date
11	4
12	6
13	8	11
14		27
15		23
16		11
17		21
18		13
19		14

We know, 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.

Also we know, orders delivered on date.

Date	Order Placed	2-day Delivery	Delivery Done on the Date
11		4
12		6
13		8	11
14	30		27
15	28		23
16	25		11
17	25		21
18	5		13
19	5		14

The cumulative or total orders booked till 19th are 337

and that of 18th are 332

=> No. orders booked on 19th are 5.

Similarly, orders on day 18th = $332 - 327 = 5$

on day 17 = $327 - 302 = 25$

on day 16 = $302 - 277 = 25$

on day 15 = $277 - 249 = 28$

on day 14 = $249 - 219 = 30$

Date	Order Placed	2-day Delivery	Lost	Delivery Done on the Date
11		4
12		6	1
13		8	2	11
14	30		12	27
15	28		12	23
16	25		2	11
17	25		9	21
18	5			13
19	5			14

Now number of orders lost -

Number of orders lost that were booked on 12th = Cumulative orders lost till 14th-Cumulative orders lost till 13th = $92-91=1$

Similairly for 13th - $92 -94 = 2$

For 14th = $106 - 94 = 12$

For 15th = $118 - 106 = 12$

For 16th = $120 - 118 = 2$

For 17th = $129 - 120 = 9$

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12		7	6	1
13		21	8	2	11
14	30	15		12	27
15	28			12	23
16	25			2	11
17	25			9	21
18	5				13
19	5				14

Now, Order till date of 13th = order booked on 12th and delivered next day + order booked on 11th and delivered after two days.

=> 11 = orders booked on 12th and delivered next day + 4

=> orders booked on 12th and delivered next day = $11 - 4 = 7$

Similairly, orders booked on 13th = $27 - 6 =21$

orders booked on 14th = $23- 8 = 15$

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12		7	6	1
13		21	8	2	11
14	30	15	3	12	27
15	28	8		12	23
16	25			2	11
17	25			9	21
18	5				13
19	5				14

Now, total orders = 1 day delivery + 2 day delivery + lost

=> on 14th

total orders = 30

1 day delivery = 15

lost = 12

=> 2 day delivery = $30-15-12 = 3$

Therefore, Order till date of 15th = order booked on 14th and delivered next day + order booked on 13th and delivered after two days.

=> order booked on 14th and delivered next day = $23 - 15 = 8$

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12		7	6	1
13		21	8	2	11
14	30	15	3	12	27
15	28	8	8	12	23
16	25	13	10	2	11
17	25	3	13	9	21
18	5	1			13
19	5				14

Doing the same for 15th :

2 day delivery = $28 -8 - 12 = 8$

=> one day delivery on 16th = $21 - 8 = 13$

=> two day delivery on 16th = $25 - 13- 2 =10$

=> One day delivery on 17th = $13 - 10 = 3$

=> Two day delivery on 17th = $25 - 3-9 = 13$

=> one day delivery on 18th = $14-13 = 1$

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12	14	7	6	1
13	31	21	8	2	11
14	30	15	3	12	27
15	28	8	8	12	23
16	25	13	10	2	11
17	25	3	13	9	21
18	5	1			13
19	5				14

From this we can say that,

total orders on 12th = $7+6+1 =14$

and total orders on 13th = $21+8+2 = 31$

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12	14	7	6	1
13	31	21	8	2	11
14	30	15	3	12	27
15	28	8	8	12	23
16	25	13	10	2	11
17	25	3	13	9	21
18	5	1			13
19	5				14

Orders lost as a fraction of orders booked was maximum on 15th day which is equal to 12/28.

Question 16

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

Question 17

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 the second day after booking. On which of the following days, was the delivery ratio the highest?

Question 18

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?

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12		7	6	1
13		21	8	2	11
14	30	15	3	12	27
15	28	8		12	23
16	25			2	11
17	25			9	21
18	5				13
19	5				14

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12		7	6	1
13		21	8	2	11
14	30	15	3	12	27
15	28	8	8	12	23
16	25	13	10	2	11
17	25	3	13	9	21
18	5	1			13
19	5				14

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12	14	7	6	1
13	31	21	8	2	11
14	30	15	3	12	27
15	28	8	8	12	23
16	25	13	10	2	11
17	25	3	13	9	21
18	5	1			13
19	5				14

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12	14	7	6	1
13	31	21	8	2	11
14	30	15	3	12	27
15	28	8	8	12	23
16	25	13	10	2	11
17	25	3	13	9	21
18	5	1			13
19	5				14

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12		7	6	1
13		21	8	2	11
14	30	15	3	12	27
15	28	8		12	23
16	25			2	11
17	25			9	21
18	5				13
19	5				14

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12		7	6	1
13		21	8	2	11
14	30	15	3	12	27
15	28	8	8	12	23
16	25	13	10	2	11
17	25	3	13	9	21
18	5	1			13
19	5				14

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12	14	7	6	1
13	31	21	8	2	11
14	30	15	3	12	27
15	28	8	8	12	23
16	25	13	10	2	11
17	25	3	13	9	21
18	5	1			13
19	5				14

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12	14	7	6	1
13	31	21	8	2	11
14	30	15	3	12	27
15	28	8	8	12	23
16	25	13	10	2	11
17	25	3	13	9	21
18	5	1			13
19	5				14

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

Solution

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CAT Past Year Questions (Topic-Wise)

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12		7	6	1
13		21	8	2	11
14	30	15	3	12	27
15	28	8		12	23
16	25			2	11
17	25			9	21
18	5				13
19	5				14

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12		7	6	1
13		21	8	2	11
14	30	15	3	12	27
15	28	8	8	12	23
16	25	13	10	2	11
17	25	3	13	9	21
18	5	1			13
19	5				14

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12	14	7	6	1
13	31	21	8	2	11
14	30	15	3	12	27
15	28	8	8	12	23
16	25	13	10	2	11
17	25	3	13	9	21
18	5	1			13
19	5				14

Date	Order Placed	1-day Delivery	2-day Delivery	Lost	Delivery Done on the Date
11			4
12	14	7	6	1
13	31	21	8	2	11
14	30	15	3	12	27
15	28	8	8	12	23
16	25	13	10	2	11
17	25	3	13	9	21
18	5	1			13
19	5				14