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.
Q. 13 Among the following days, the largest fraction of orders booked on which day was lost?
1) 14th 2) 13th 3) 15th 4) 16th
Q. 14 On which of the following days was the number of orders booked the highest?
1) 14th 2) 13th 3) 12th 4) 15th
Q. 15 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) 16th 2) 15th 3) 13th 4) 14th
Q. 16 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) 13th 2) 14th 3) 16th 4) 15th
🔹 Step 0: Understand What’s Given
The original table gives:
- Cumulative orders booked
- Orders delivered on each day
- Cumulative orders lost
You’re also told:
- An order is either delivered next day or two days later.
- If not delivered by end of second day → lost
- You can compute how many orders were booked or lost on a particular day by subtracting cumulative values.
🔹 Step 1: Calculate “Orders booked on that day”
Use:
Orders booked on Day D = Cumulative booked on Day D – Cumulative booked on Day (D–1)
Example:
- 14th: 249 – 219 = 30
- 15th: 277 – 249 = 28
- 16th: 302 – 277 = 25
- 17th: 327 – 302 = 25
- 18th: 332 – 327 = 5
- 19th: 337 – 332 = 5
For 13th: Directly take cumulative = 219 (start of the dataset)
✅ Filled first column: “Orders booked on that day”
🔹 Step 2: Calculate “Orders lost on that day”
Use:
Orders lost on Day D = Cumulative lost on Day D – Cumulative lost on Day (D–1)
Example:
- 14th: 92 – 91 = 1
- 15th: 94 – 92 = 2
- 16th: 106 – 94 = 12
- 17th: 118 – 106 = 12
- 18th: 120 – 118 = 2
- 19th: 129 – 120 = 9
For 13th: Cumulative = 91 → Lost that day = 91
✅ Filled last column: “Orders declared lost on that day”
🔹 Step 3: Use Delivery logic to backtrack deliveries
From prompt:
- Orders are delivered on day +1 or day +2
- Use the given “Orders delivered on day” to deduce what was booked 1 day or 2 days prior
Let’s take an example:
🔹 Day 14th:
- Delivered: 27
- We’re told: 6 orders booked on 12th were delivered on 14th (i.e. took 2 days)
→ So, rest were booked on 13th (i.e. took 1 day)
→ 27 – 6 = 21
✅ So, 21 orders booked on 13th were delivered after 1 day
→ For Day 14:
- Delivery of 1 day prior (13th) = 21
- Delivery of 2 days prior (12th) = 6
🔹 Day 15th:
- Delivered: 23
- We’re told 8 orders booked on 13th were delivered after 2 days (i.e. on 15th)
→ So 23 – 8 = 15 from 14th (delivered after 1 day)
✅ Day 15:
- Delivery of 1 day prior = 15 (booked on 14th)
- Delivery of 2 days prior = 8 (booked on 13th)
🔹 Day 16th:
Delivered: 11
Lost on 16th: 12
We earlier computed:
- Orders booked on 14th = 30
→ 1 lost on 14th (from column), so 29 remained
→ 21 delivered on 14th (already recorded), so 30 – 21 – 1 = 8 delivered on 15th
From image:
→ Delivery of 1 day prior = 8
→ Delivery of 2 days prior = 3
→ Lost = 2 (so 25 were booked on 15th, 20 delivered, 2 lost, 3 leftover)
✅ Day 16:
- Delivery of 1 day prior = 8
- Delivery of 2 days prior = 3
Use same logic for 17th to 19th based on previous day bookings and losses.
🔹 Final Structure:
| Day | Orders booked | Delivery of 1 day prior | Delivered on day | Delivery of 2 days prior | Orders lost on that day |
|---|---|---|---|---|---|
| 13th | 31 | 7 | 11 | 4 | 2 |
| 14th | 30 | 21 | 27 | 6 | 1 |
| 15th | 28 | 15 | 23 | 8 | 2 |
| 16th | 25 | 8 | 11 | 3 | 12 |
| 17th | 25 | 13 | 21 | 8 | 12 |
| 18th | 5 | 3 | 13 | 10 | 2 |
| 19th | 5 | 1 | 14 | 13 | 9 |
🔁 Summary of Steps:
| Step | Action |
|---|---|
| 1️⃣ | Subtract cumulative values to get “orders booked” and “orders lost” per day |
| 2️⃣ | Use total orders delivered on day = delivery from 1-day-prior + 2-days-prior |
| 3️⃣ | Use known delivery delays (given for 11th–13th) to deduce deliveries from earlier bookings |
| 4️⃣ | Subtract known values from delivered to compute deliveries from one-day or two-day prior |
| 5️⃣ | Fill remaining deliveries using constraints that lost = not delivered by second day |
🔹 Q13: Largest fraction of orders booked on a day that were lost
We use:
Fraction lost = Orders lost on day / Orders booked on day
Let’s compute:
- 13th: 2 / 31 ≈ 0.0645
- 14th: 1 / 30 ≈ 0.033
- 15th: 12 / 28 ≈ 0.4285 ✅
- 16th: 2 / 25 = 0.08
🟩 Answer: (3) 15th (largest loss fraction)
🔹 Q14: Day with highest number of orders booked
From table:
- 13th: 31
- 14th: 30
- 15th: 28
- 16th: 25
🟩 Answer: (2) 13th
🔹 Q15: Delivery ratio = Delivered next day / Delivered 2 days after booking
We use:
Delivery ratio = x / y where
- x = Delivered next day
- y = Delivered 2 days after
Let’s compute:
- 13th: 7 / 4 = 1.75
- 14th: 21 / 6 = 3.5 ✅
- 15th: 15 / 8 = 1.875
- 16th: 8 / 3 ≈ 2.67
🟩 Answer: (4) 14th (highest delivery ratio)
🔹 Q16: Average delivery time = (x + 2y) / (x + y)
Let’s compute:
- 13th: (7 + 8) / (7 + 4) = (7 + 2×4) / (7 + 4) = (7 + 8)/11 = 15 / 11 ≈ 1.36
- 14th: (21 + 12)/27 = 33 / 27 ≈ 1.22 ✅
- 15th: (15 + 16)/23 = 31 / 23 ≈ 1.35
- 16th: (8 + 6)/11 = 14 / 11 ≈ 1.27
🟩 Answer: (2) 14th (least average time)
✅ Final Answers Recap:
| Q. No | Answer | Reason |
|---|---|---|
| 13 | (3) 15th | Highest loss fraction = 12/28 |
| 14 | (2) 13th | Highest bookings = 31 |
| 15 | (4) 14th | Highest delivery ratio = 21/6 |
| 16 | (2) 14th | Least avg. delivery time ≈ 1.22 |
Let me know if you’d like a visual chart/graph representation or want the table exported.
