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
Question: 1
Among the following days, the largest fraction of orders booked on which day was lost?
\(14^{th}\) day \(⇒\)\(30\) Booked \(⇒\)\(12\) loss \(⇒\)\(\frac{12}{30}\)
\(13^{th}\) day \(⇒\)\(31\) Booked \(⇒\)\(2\) loss \(⇒ \frac{2}{31}\)
\(16^{th}\) day \(⇒ 25\) Booked \(⇒ 2\) loss \(⇒ \frac{2}{25}\)
\(15^{th}\) day \(⇒ 28\) Booked \(⇒ 12\) loss \(⇒ \frac{12}{28}\)
The highest value is \(\frac{12}{28}\), on the \(15^{th}\) day.
Was this answer helpful?
0
0
Hide Solution
Verified By Collegedunia
Approach Solution -2
On the 19th, the total number of orders booked was 337, while on the 18th it was 332. This means 5 orders were booked on the 19th. We can similarly calculate the number of orders booked each day until the 14th.
To find the number of orders lost that were booked on the 12th:
Subtract the cumulative orders lost by the 13th from those lost by the 14th: 92−91=192−91=1.
We can find the number of orders lost each day up to the 17th in a similar way.
On the 13th, 11 orders were delivered. Of these, 4 were booked on the 11th, so 7 were booked on the 12th.
We can find out how many orders took 1 day and 2 days to be delivered up to the 17th in a similar way.
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
On the 12th, the total number of orders booked was 7+6+1=147+6+1=14.
The fractions of orders lost for each day are:
On the 15th: 12282812
On the 16th: 225252
On the 13th: 231312
On the 14th: 830308
Based on these fractions, Option C seems to be the correct answer.
Was this answer helpful?
0
0
Question: 2
On which of the following days was the number of orders booked the highest?
On the 19th, the total number of orders booked was 337, while on the 18th it was 332. This means 5 orders were booked on the 19th. We can similarly calculate the number of orders booked each day until the 14th.
To find the number of orders lost that were booked on the 12th:
Subtract the cumulative orders lost by the 13th from those lost by the 14th: 92−91=192−91=1.
We can find the number of orders lost each day up to the 17th in a similar way.
On the 13th, 11 orders were delivered. Of these, 4 were booked on the 11th, so 7 were booked on the 12th.
We can find out how many orders took 1 day and 2 days to be delivered up to the 17th in a similar way.
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
The total number of orders booked on the 12th is 7+6+1=147+6+1=14.
The total number of orders placed on the 13th is 21+8+2=3121+8+2=31.
From the table, we can see that the number of orders booked on the 13th is the highest among the options.
Was this answer helpful?
0
0
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?
Delivery ratio = \(\frac{Next \;day}{day \;after}\)
a. \(13^{th}\) day \(⇒ \frac{21}{8}\)
b. \(15^{th}\) day \(⇒ \frac{8}{8}\)
c. \(14^{th}\) day \(⇒ \frac{15}{3}\)
d. \(16^{th}\) day = \(\frac{13}{10}\)
The highest ratio is \(\frac{15}{3}\), on \(14^{th}\) day.
Was this answer helpful?
0
0
Hide Solution
Verified By Collegedunia
Approach Solution -2
On the 19th, the total number of orders booked was 337, while on the 18th it was 332. This means 5 orders were booked on the 19th. We can similarly calculate the number of orders booked each day until the 14th.
To find the number of orders lost that were booked on the 12th:
Subtract the cumulative orders lost by the 13th from those lost by the 14th: 92−91=192−91=1.
We can find the number of orders lost each day up to the 17th in a similar way.
On the 13th, 11 orders were delivered. Of these, 4 were booked on the 11th, so 7 were booked on the 12th.
We can find out how many orders took 1 day and 2 days to be delivered up to the 17th in a similar way.
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
In simpler terms:
On the 12th, a total of 14 orders were booked.
Looking at the table, we can see that among the given options, the highest number of orders was booked on the 13th.
Delivery ratios can be calculated for each day:
On the 15th, the delivery ratio is 88=188=1.
On the 16th, the delivery ratio is 1310=1.31013=1.3.
On the 13th, the delivery ratio is 218=2.625821=2.625.
On the 14th, the delivery ratio is 153=5315=5.
Thus, based on the delivery ratios, Option C seems to be the most suitable choice.
Was this answer helpful?
0
0
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 (x+2y)/(x+y). On which of the following days was the average time taken to deliver orders booked the least?
On the 19th, the total number of orders booked was 337, while on the 18th it was 332. This means 5 orders were booked on the 19th. We can similarly calculate the number of orders booked each day until the 14th.
To find the number of orders lost that were booked on the 12th:
Subtract the cumulative orders lost by the 13th from those lost by the 14th: 92−91=192−91=1.
We can find the number of orders lost each day up to the 17th in a similar way.
On the 13th, 11 orders were delivered. Of these, 4 were booked on the 11th, so 7 were booked on the 12th.
We can find out how many orders took 1 day and 2 days to be delivered up to the 17th in a similar way.
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
On the 12th, the total number of orders booked was 7+6+1=147+6+1=14.
From the table, we can see that among the options, the highest number of orders were booked on the 13th.
To calculate the average delivery time:
On the 15th, the delivery ratio is 88=188=1.
On the 16th, the delivery ratio is 1310=1.31013=1.3.
On the 13th, the delivery ratio is 218=2.625821=2.625.
On the 14th, the delivery ratio is 153=5315=5.
Based on these delivery ratios, we can determine the average delivery time.
