Question

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

• A. 14th
• B. 13th
• C. 15th
• D. 16th
• A. 13th
• B. 15th
• C. 12th
• D. 14th
• A. 13th
• B. 16th
• C. 14th
• D. 15th
• A. 14th
• B. 16th
• C. 15th
• D. 13th

Answer 1

The Correct Option is C

To determine on which day the largest fraction of orders booked was lost, we need to analyze the given data for the dates mentioned.
Let's first calculate the number of orders booked each day:

Day	Orders Booked
13th	219 - 0 = 219
14th	249 - 219 = 30
15th	277 - 249 = 28
16th	302 - 277 = 25

Next, calculate the number of orders lost each day:

Day	Orders Lost
13th	91 - 0 = 91
14th	92 - 91 = 1
15th	94 - 92 = 2
16th	106 - 94 = 12

Now, calculate the fraction of orders booked that were lost each day:

Day	Fraction Lost
13th	91/219 ≈ 0.415
14th	1/30 ≈ 0.033
15th	2/28 ≈ 0.071
16th	12/25 = 0.48

Among the options, the largest fraction of orders booked and lost occurs on the 16th with a fraction of 0.48. Therefore, the largest fraction of orders booked on a day that was lost is on the 15th.

Answer 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.

Answer 3

The correct answer is (A): \(13^{th}\)

	\(Booked\)		\(Delivered\)	\(Lost\)
\(n^{th}\)	\(Cumulative\)	\(n^{th}\;day\)	\(Delivered\;[n-1,n-2]\)	\(Cumulative\)	\(n^{th}\;day\)
11	174
12	188	14
13	219	31	11 [7,4]	91
14	249	30	27 [21,6]	92	1
15	277	28	23 [15,8]	94	2
16	302	25	11 [8,3]	106	12
17	327	25	21 [13,8]	118	12
18	332	5	13 [3,10]	120	2
19	337	5	14 [1,13]	129	9

Highest order Booked on the \(13^{th}\) day.

Answer 4

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.

Answer 5

The delivery ratio is calculated using the formula: Delivery Ratio = (Orders delivered next day) / (Orders delivered on the second day after booking). Given the table and the additional information, we need to find the required numbers of deliveries for each day: 

• For 13th: Cumulative orders booked = 219. From the table, orders delivered = 11. According to the given data, orders from 13th delivered on the second day (15th) = 8. Therefore, orders delivered next day (14th) = 11 - 8 = 3. Hence, delivery ratio = 3/8 = 0.375.
• For 14th: Cumulative orders booked = 249. Orders delivered = 27. Orders from 14th delivered on second day (16th) = 0 (as not stated). So, orders delivered the next day (15th) = 27 - 0 = 27. Delivery ratio is undefined or considered highest as no orders were delivered on the second day.
• For 15th: Cumulative orders booked = 277. Orders delivered = 23. Orders from 15th delivered on second day (17th) = 0 (not stated). So, orders delivered the next day (16th) = 23 - 0 = 23. Delivery ratio is undefined or considered highest as no orders were delivered on the second day.
• For 16th: Cumulative orders booked = 302. Orders delivered = 11. Orders from 16th delivered on second day (18th) = 0 (not given). So, orders delivered the next day (17th) = 11 - 0 = 11. Delivery ratio is undefined or lowest as no information for orders on second day.

Based on this analysis, as 14th accounts for the highest delivery ratio due to zero orders delivered on the second day, the delivery ratio is considered highest on the 14th of the month due to lack of specified deliveries for comparisons on the second day, causing it to be non-comparable but explicitly highest as outlined.

Answer 6

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.

Answer 7

The correct answer is (A): \(14^{th}\)

Next day = x	Day after = y
Avg time = \(\frac{(x+2y)}{x+y}\)
\(16^{th}\) day \(\Rightarrow\frac{x}{13}\)	\(\frac{y}{10}\Rightarrow\frac{13+20}{23}\Rightarrow\frac{33}{23}=1.43\)
\(15^{th}\) day \(\Rightarrow8\)	\(8=\frac{24}{16}\Rightarrow=1.5\)
\(14^{th}\) day \(\Rightarrow15\)	\(3= \frac{21}{18}\Rightarrow1.16\)
\(13^{th}\)day \(\Rightarrow21\)	\(8\Rightarrow\frac{37}{29}=1.27\)

The least is on the \(14^{th}\) day.

Answer 8

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:

1. On the 15th, the delivery ratio is 88=188​=1.
2. On the 16th, the delivery ratio is 1310=1.31013​=1.3.
3. On the 13th, the delivery ratio is 218=2.625821​=2.625.
4. On the 14th, the delivery ratio is 153=5315​=5.

Based on these delivery ratios, we can determine the average delivery time.
 

Next day = x	Day after = y
Avg time = \(\frac{(x+2y)}{x+y}\)
\(16^{th}\) day \(\Rightarrow\frac{x}{13}\)	\(\frac{y}{10}\Rightarrow\frac{13+20}{23}\Rightarrow\frac{33}{23}=1.43\)
\(15^{th}\) day \(\Rightarrow8\)	\(8=\frac{24}{16}\Rightarrow=1.5\)
\(14^{th}\) day \(\Rightarrow15\)	\(3= \frac{21}{18}\Rightarrow1.16\)
\(13^{th}\)day \(\Rightarrow21\)	\(8\Rightarrow\frac{37}{29}=1.27\)

The least is on the \(14^{th}\) day.