Routes and Network MCQ Quiz - Objective Question with Answer for Routes and Network - Download Free PDF
Last updated on Mar 21, 2025
Latest Routes and Network MCQ Objective Questions
Routes and Network Question 1:
Comprehension:
In the magical town of Hogwartz, the road network is designed to facilitate smooth travel between various parts of the town. The roads are organized as follows:
i. The roads are categorized into two types: north-south roads and east-west roads.
ii. All north-south roads run parallel to each other, and similarly, all east-west roads are parallel to one another.
iii. The north-south roads are labeled alphabetically starting from 'A' for the westernmost road, progressing through B, C, D, and so on.
iv. The east-west roads are numbered sequentially, with 1 being assigned to the southernmost road and increasing in number as they go north.
v. Every intersection where two roads meet is referred to as a "square." The name of each square is formed by combining the labels of the intersecting roads. For example, the square where road C intersects with road 5 is labeled as C5. The distance between any two consecutive squares is fixed at 1 km.
vi. Currently, all roads are bidirectional. However, the government has the authority to convert any road to one-way in response to traffic management needs.
vii. U-turns are prohibited at all intersections (squares).
All even-numbered roads are now one-way, allowing travel only towards the west, while odd-numbered roads are one-way, allowing travel only towards the east. Additionally, roads D and F are designated as one-way, with road D allowing only northward travel and road F allowing only southward travel. Based on this setup, at which of the following squares can the person heading east not be located?
Answer (Detailed Solution Below)
Routes and Network Question 1 Detailed Solution
Let’s consider each option one by one.
Option 1, i.e., D3 -> Since road 3 is made one way towards the east, this is a possible position.
Option 2, i.e., D4 -> Since road 4 is made one way towards the west, this is not possible.
Option 3, i.e., E3 -> Since road 3 is made one way towards east, this is possible.
Option 4, i.e., F1 -> Since road 1 is made one way towards east, this is possible.
Hence, option (2) is correct.
Routes and Network Question 2:
Comprehension:
In the magical town of Hogwartz, the road network is designed to facilitate smooth travel between various parts of the town. The roads are organized as follows:
i. The roads are categorized into two types: north-south roads and east-west roads.
ii. All north-south roads run parallel to each other, and similarly, all east-west roads are parallel to one another.
iii. The north-south roads are labeled alphabetically starting from 'A' for the westernmost road, progressing through B, C, D, and so on.
iv. The east-west roads are numbered sequentially, with 1 being assigned to the southernmost road and increasing in number as they go north.
v. Every intersection where two roads meet is referred to as a "square." The name of each square is formed by combining the labels of the intersecting roads. For example, the square where road C intersects with road 5 is labeled as C5. The distance between any two consecutive squares is fixed at 1 km.
vi. Currently, all roads are bidirectional. However, the government has the authority to convert any road to one-way in response to traffic management needs.
vii. U-turns are prohibited at all intersections (squares).
If all even-numbered roads are now one-way with traffic only allowed to travel west, and all odd-numbered roads are one-way only towards the east, with roads D and F restricted to one-way traffic towards the north and south, respectively. Dobby's car starts from D1, and Harry's car starts from E4, both traveling at equal speeds. After each of them travels 4 km, at which square can they meet?
Answer (Detailed Solution Below)
Routes and Network Question 2 Detailed Solution
Let's consider each option;
Option 1, i.e., D4 -> Minimum travelling distance between D1 and D4 is 3 km (an odd number). So, it cannot be covered by travelling 4 km (an even number).
Option 2, i.e., E3 -> Minimum travelling distance between D1 and E3 is 3 km (an odd number). So, it cannot be covered by travelling 4 km (an even number).
Option 3, i.e., F3 -> Minimum travelling distance between D1 and F3 (an even number) is 4 km and the minimum travelling distance between E4 and F3 is 2 km (an even number). So, it can be covered by travelling 4 km (an even number) as shown in the figure.
Option 4, i.e., C3 -> Minimum travelling distance between D1 and C3 is 3 km (an odd number). So, it cannot be covered by travelling 4 km (an even number).
Hence, option (3) is correct.
Routes and Network Question 3:
Comprehension:
In the magical town of Hogwartz, the road network is designed to facilitate smooth travel between various parts of the town. The roads are organized as follows:
i. The roads are categorized into two types: north-south roads and east-west roads.
ii. All north-south roads run parallel to each other, and similarly, all east-west roads are parallel to one another.
iii. The north-south roads are labeled alphabetically starting from 'A' for the westernmost road, progressing through B, C, D, and so on.
iv. The east-west roads are numbered sequentially, with 1 being assigned to the southernmost road and increasing in number as they go north.
v. Every intersection where two roads meet is referred to as a "square." The name of each square is formed by combining the labels of the intersecting roads. For example, the square where road C intersects with road 5 is labeled as C5. The distance between any two consecutive squares is fixed at 1 km.
vi. Currently, all roads are bidirectional. However, the government has the authority to convert any road to one-way in response to traffic management needs.
vii. U-turns are prohibited at all intersections (squares).
In Hogwartz Town, all even-numbered roads are now one-way, with traffic moving only towards the west, while odd-numbered roads are one-way only towards the east. Additionally, roads D and F are one-way towards the north and south, respectively. If Voldemort needs to travel from D2 to F4, how many distinct paths can he take to cover the least distance, considering the new road restrictions?
Answer (Detailed Solution Below) 3
Routes and Network Question 3 Detailed Solution
The minimum distance from D2 to F4 is 6 km with one-way restrictions. So, we have to figure out different ways with which we can travel 6 km to reach from D2 to F4.
As shown in the figure, it can be done in three ways.
Routes and Network Question 4:
Comprehension:
In the magical town of Hogwartz, the road network is designed to facilitate smooth travel between various parts of the town. The roads are organized as follows:
i. The roads are categorized into two types: north-south roads and east-west roads.
ii. All north-south roads run parallel to each other, and similarly, all east-west roads are parallel to one another.
iii. The north-south roads are labeled alphabetically starting from 'A' for the westernmost road, progressing through B, C, D, and so on.
iv. The east-west roads are numbered sequentially, with 1 being assigned to the southernmost road and increasing in number as they go north.
v. Every intersection where two roads meet is referred to as a "square." The name of each square is formed by combining the labels of the intersecting roads. For example, the square where road C intersects with road 5 is labeled as C5. The distance between any two consecutive squares is fixed at 1 km.
vi. Currently, all roads are bidirectional. However, the government has the authority to convert any road to one-way in response to traffic management needs.
vii. U-turns are prohibited at all intersections (squares).
Starting from square G2, Snape travels a total distance of 6 km. Which of the following squares could not be his destination?
Answer (Detailed Solution Below)
Routes and Network Question 4 Detailed Solution
Calculate the steps to each of the given points in the options, hence, I5 is the only point, where Snape can't reach by travelling 6 km.
Routes and Network Question 5:
Comprehension:
In the magical town of Hogwartz, the road network is designed to facilitate smooth travel between various parts of the town. The roads are organized as follows:
i. The roads are categorized into two types: north-south roads and east-west roads.
ii. All north-south roads run parallel to each other, and similarly, all east-west roads are parallel to one another.
iii. The north-south roads are labeled alphabetically starting from 'A' for the westernmost road, progressing through B, C, D, and so on.
iv. The east-west roads are numbered sequentially, with 1 being assigned to the southernmost road and increasing in number as they go north.
v. Every intersection where two roads meet is referred to as a "square." The name of each square is formed by combining the labels of the intersecting roads. For example, the square where road C intersects with road 5 is labeled as C5. The distance between any two consecutive squares is fixed at 1 km.
vi. Currently, all roads are bidirectional. However, the government has the authority to convert any road to one-way in response to traffic management needs.
vii. U-turns are prohibited at all intersections (squares).
Hermione is traveling from square H6 to square B2 in Hogwartz town, with a stop at square D4 to visit Harry along the way. What is the minimum distance she must travel, given the road network in the town?
Answer (Detailed Solution Below)
Routes and Network Question 5 Detailed Solution
The road diagram of the town is given in the diagram:
To reach B2 from H6, the person must walk 6 steps towards the west and 4 steps towards the south, regardless of the route chosen.
Thus, the possible paths she can take are:
H6 → D6 → D4 → B4 → B2 or
H6 → H4 → D4 → B4 → B2
(There may be a few other routes with the same total distance.)
Top Routes and Network MCQ Objective Questions
In the following question, select the related figure from the given alternatives.
Answer (Detailed Solution Below)
Routes and Network Question 6 Detailed Solution
Download Solution PDFThe movement of symbols is as follows:
The symbol at position 1 will duplicate and move at position 9 and 6. The symbol at position 9 will duplicate and place at 4 and 3. The symbol at position 3 will move at position 5. The symbol at position 5 will move at position 7. The symbol at position 7 will move at position 1. The final figure will be as follows:
Comprehension:
Every day a widget supplier supplies widgets from the warehouse (W) to four locations – Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
If the last location visited is Ahmednagar, then what is the total distance covered in the route (in km)?
Answer (Detailed Solution Below) 35
Routes and Network Question 7 Detailed Solution
Download Solution PDFIn the given question key points to be noted are:
1) The supplier starts from the warehouse (W). The travel route is determined by the demand at each location, visiting locations in decreasing order of demand. In case of a tie in demand values, the supplier chooses the closest location.
2) The supplier can choose between a direct path or a path via the warehouse. The supplier will always choose the path with the minimum distance.
3) For each combination, determine the sequence of locations to visit based on the descending order of demand. Resolve ties by choosing the closest location.
4) For the given question, we will refer to Ahmednagar, Bikrampore, Chitrachak, and Deccan Park as A,B,C and D resp.
Now it is given that, "If the last location visited is Ahmednagar, then what is the total distance covered in the route (in km)?"
⇒ Ahmednagar is the last location, thus the demand in A must be 50, because if it were demand in B and D would be less than A and we won't visit A last.
| 1st | 2nd | 3rd | 4th | |
| Warehouse (W) | (A) |
Next, we can deduce that 1st city to be travelled will be C because even when demanding 70 it is higher than other cities.
| 1st | 2nd | 3rd | 4th | |
| Warehouse (W) | (C) | (A) |
∴ Distance (W-C) = 12
Next city to be travelled will be B because it will have a demand of 60 ( demand ≠ 40 because demand of A = 50).
(shortest route will be direct.)
Thus, the 3rd city to be visited will be D.
travelling from B to D only route will be through the warehouse.
| 1st | 2nd | 3rd | 4th | |
| Warehouse (W) | (C) | (B) | (D) | (A) |
∴ Distance (W-C-B-W-D) = 12 + 4 + 10 + 2
travelling from D to A : we will have two routes direct (8km) and through warehouse (2+5=7km). we will take the shortest path.
| 1st | 2nd | 3rd | 4th | |
| Warehouse (W) | (C) | (B) | (D) | (A) |
∴ Final Distance (W-C-B-W-D-W-A) = 12 + 4 + 10 + 2 + 5 = 35
Sateja took her four grandchildren for a car ride and they visited six junctions. When she asked each of them to draw road maps that they used during their ride, they produced the following maps though all did not show exact relative positions of road connections. If only three maps are correct, then select the map with incorrect connections.
Answer (Detailed Solution Below)
Routes and Network Question 8 Detailed Solution
Download Solution PDFOption(1) is the answer.
Except for option(1), every map shows four 3-road junctions and two 2-road junctions while option(1) shows all junctions have 3-road junctions.
Hence the correct answer is an option(1) i.e.,
I live in a village Pali and I want to visit my therapy clients living in nearby villages Neli, Teli and Seli. All villages are connected by two-way routes. The length of the route from Pali to Neli is 31 km, from Teli to Pali is 20 km, from Seli to Pali is 22 km, from Neli to Teli is 16 km, from Teli to Seli 18 km, and from Seli to Neli is 26 km long. Select. the minimum distance, in km, that I require to cover to visit my clients and return to Pali.
Answer (Detailed Solution Below)
Routes and Network Question 9 Detailed Solution
Download Solution PDFOption(1) is answer.
There are six possibilities to visit clients and return to pali.
(1) Pali - Neli - Seli - Teli - Pali
Distance = 31 Km + 26 Km + 18 Km + 20 Km = 95 Km
(2) Pali - Neli - Teli - Seli - Pali
Distance = 31 Km + 16 Km + 18 Km + 22 Km = 87 Km
(3) Pali - Teli - Neli - Seli - Pali
Distance = 20 Km + 16 Km + 26 Km + 22 Km = 84 Km
(4) Pali - Teli - Seli - Neli - Pali
Distance = 20 Km + 18 Km + 26 Km + 31 Km = 95 Km
(5) Pali - Seli - Neli - Teli - Pali
Distance = 22 Km + 26 Km + 16 Km + 20 Km = 84 Km
(6) Pali - Seli - Teli - Neli - Pali
Distance = 22 Km + 18 Km + 16 Km + 31 Km = 87 Km
So, the minimum distance to visit clients and return to pali is 84 Km.
Hence, the correct answer is option(1) i.e., 84 Km.
Alternate Method
Option(1) is answer.
For the minimum distance, we need to eliminate the path that has a maximum length.
Here we need to avoid the path of Neli to Pali i.e. 31 Km. So we have two options :
(1) Pali - Teli - Neli - Seli - Pali
Distance = 20 Km + 16 Km + 26 Km + 22 Km = 84 Km
(2) Pali - Seli - Neli - Teli - Pali
Distance = 22 Km + 26 Km + 16 Km + 20 Km = 84 Km
So, the minimum distance to visit clients and return to Pali is 84 Km.
Hence, the correct answer is option(1) i.e., 84 Km.
A road map connecting to the colonies A, B, C, D and E is shown in the figure below. Design the route starting from any colony of your choice so that you will have to walk on each of the seven routes once and only once. The starting point and the end point may not be the same. From how many points, can such route be started ?
Answer (Detailed Solution Below)
Routes and Network Question 10 Detailed Solution
Download Solution PDFOption(3) is answer.
For this question, we can take all points one by one.
Such route started from Point A: Yes it exists, route ACDEBDAB, etc.
Such route started from Point B: Yes it exist , route BADEBDCA, etc.
Such route started from Point C: No it does not exist.
Such route started from Point D: No it does not exist.
Such route started from Point E: No it does not exist.
So, such route is started only from two points i.e., A and B.
Hence, the correct answer is option(3)i.e. Two.
Important Points
- For such routes we need points that have odd number of junction.
In an office, two phones P1 and P2 are connected to LAN. L1 and L2 respectively. If the LAN is not in operation, then both the phones can be used for tele communication. There are three computers C1, C2 and C3 with which LAN L1 & L2 are directly connected L1 can be used for C1 and C2. L2 can be sued for C1 and C3. If L1 is not in operation which of the following operations will not be performed.
Answer (Detailed Solution Below)
Routes and Network Question 11 Detailed Solution
Download Solution PDFIn an office, two phones P1 and P2 are connected to LAN L1 & L2 respectively. If LAN is not in operation, the both the phones can be used for telecommunication.
→ L1 can be used for computer C1 and C2 only
→ L2 can be used for computer C1 and C3 only
If L1 is not in operation, then P1 (telecom) will work and C1 will work with network of L2. So, only network of C2 will not network.
Comprehension:
Every day a widget supplier supplies widgets from the warehouse (W) to four locations – Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
If Ahmednagar is not the first location to be visited in a route and the total route distance is 29 km, then which of the following is a possible number of widgets delivered on that day?
Answer (Detailed Solution Below)
Routes and Network Question 12 Detailed Solution
Download Solution PDFIn the given question key points to be noted are:
1) The supplier starts from the warehouse (W). The travel route is determined by the demand at each location, visiting locations in decreasing order of demand. In case of a tie in demand values, the supplier chooses the closest location.
2) The supplier can choose between a direct path or a path via the warehouse. The supplier will always choose the path with the minimum distance.
3) For each combination, determine the sequence of locations to visit based on the descending order of demand. Resolve ties by choosing the closest location.
4) For the given question, we will refer to Ahmednagar, Bikrampore, Chitrachak, and Deccan Park as A,B,C and D resp.
Now, it has been given that "If Ahmednagar is not the first location to be visited in a route and the total route distance is 29 km, then which of the following is a possible number of widgets delivered on that day?"
Here, it has been given that A is not the first city to be visited, thus C will be the first city to be visited.
now, we will have to look at various cases to find the suitable one.
CASE 1: C = 100, A= 70, followed by B and D in any sequence.
⇒ Total Distance will always be greater than 29 because the distance covered from W-C-W-A = 12 + 12 + 5 =29.
CASE 2: C = 100 or 70 , A = 50 , D = 50 , B = 40 (W-C-D-W-A-B)
⇒ Total Distance = 12 + 6 + 2 + 5 + 6 = 31
CASE 3: C= 100 or 70 , A= 50 , B=60 , D= 50 or 30 (W-C-B-A-W-D)
⇒ Total Distance = 12 + 4 + 6 + 2 + 5 = 29
∴ Case 3 will fulfill the situation.
⇒ POSSIBLE NUMBER OF WIDGETS SOLD
(100+50+60+50) = 260, or
(100+50+60+30) = 240, or
(70+50+60+50) = 230, or
(70+50+60+30) = 210
∴ Solution is 210.
Comprehension:
Every day a widget supplier supplies widgets from the warehouse (W) to four locations – Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
If the first location visited from the warehouse is Ahmednagar, then what is the chance that the total distance covered in the route is 40 km?
Answer (Detailed Solution Below)
Routes and Network Question 13 Detailed Solution
Download Solution PDFIn the given question key points to be noted are:
1) The supplier starts from the warehouse (W). The travel route is determined by the demand at each location, visiting locations in decreasing order of demand. In case of a tie in demand values, the supplier chooses the closest location.
2) The supplier can choose between a direct path or a path via the warehouse. The supplier will always choose the path with the minimum distance.
3) For each combination, determine the sequence of locations to visit based on the descending order of demand. Resolve ties by choosing the closest location.
4) For the given question, we will refer to Ahmednagar, Bikrampore, Chitrachak, and Deccan Park as A,B,C and D resp.
Now, it has been given that "If the first location visited from the warehouse is Ahmednagar, then what is the chance that the total distance covered in the route is 40 km?"
Here, it has been given that first city to be visited is A, thus it has the highest demand i.e. 70 and this makes the demand of C ≤ A ⇒ C = 70
the first two cities visited will be A followed by C, thus the possible sequences can be:
1) W-A-W-C-B-W-D : in this case, B and D will have demands of 60 and 50 resp.
⇒ Total Distance = 5 + 5 + 12 + 4 +10 + 2 = 38
2) W-A-W-C-D-W-B : in this case, D and B will have demands 50 and 40 resp.
⇒ Total Distance = 5 + 5+ 12 + 6 + 10 + 2 = 40
∴ Case 2 will fulfill the situation.
⇒ Probability of sequence W-A-W-C-D-W-B = (0.6)(0.3) = 0.18 =18%
Mistake Points Here, we will consider the probabilities of D and B only. Because the order that city A will be visited first followed by city C has been given, thus, they are "sure events" with probability of happening = 1.
Comprehension:
Every day a widget supplier supplies widgets from the warehouse (W) to four locations – Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
What is the chance that the total number of widgets delivered in a day is 260 units and the route ends at Bikrampore?
Answer (Detailed Solution Below)
Routes and Network Question 14 Detailed Solution
Download Solution PDFIn the given question key points to be noted are:
1) The supplier starts from the warehouse (W). The travel route is determined by the demand at each location, visiting locations in decreasing order of demand. In case of a tie in demand values, the supplier chooses the closest location.
2) The supplier can choose between a direct path or a path via the warehouse. The supplier will always choose the path with the minimum distance.
3) For each combination, determine the sequence of locations to visit based on the descending order of demand. Resolve ties by choosing the closest location.
4) For the given question, we will refer to Ahmednagar, Bikrampore, Chitrachak, and Deccan Park as A,B,C and D resp.
Now, it has been given that "What is the chance that the total number of widgets delivered in a day is 260 units and the route ends at Bikrampore?"
the maximum number of widgets that the warehouse can deliver = 70(A) + 60(B) + 100(C) + 50(D) = 280
And we according to the question 260 widgets will be delivered i.e. 20 less widgets that the maximum output, and B is the last city to visited i.e. least demand.
⇒ This 20 can be decreased from B because that would make the total widgets delivered 260 and D the least demanding city.
Thus, the number of widgets to be delivered at A , B , C and D will be 70 , 40 , 100 , 50 respectively.
⇒ The sequence will be in decreasing order of demand: C-A-B-D
⇒ The probability of this A, B, C and D having demands 70, 40, 100 and 50 resp. ⇒ P(A)=0.6 P(B)=0.3 P(C)=0.7 P(D)=0.6
∴ P(C-A-B-D) = (0.6)(0.3)(0.7)(0.6) = 0.0756 = 7.56%
Comprehension:
Every day a widget supplier supplies widgets from the warehouse (W) to four locations – Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
If the total number of widgets delivered in a day is 250 units, then what is the total distance covered in the route (in km)?
Answer (Detailed Solution Below) 38
Routes and Network Question 15 Detailed Solution
Download Solution PDFIn the given question key points to be noted are:
Th1) The supplier starts from the warehouse (W). The travel route is determined by the demand at each location, visiting locations in decreasing order of demand. In case of a tie in demand values, the supplier chooses the closest location.
2) The supplier can choose between a direct path or a path via the warehouse. The supplier will always choose the path with the minimum distance.
3) For each combination, determine the sequence of locations to visit based on the descending order of demand. Resolve ties by choosing the closest location.
4) For the given question, we will refer to Ahmednagar, Bikrampore, Chitrachak, and Deccan Park as A,B,C and D resp.
Now, it has been given that "If the total number of widgets delivered in a day is 250 units, then what is the total distance covered in the route (in km)?"
the maximum number of widgets that the warehouse can deliver = 70(A) + 60(B) + 100(C) + 50(D) = 280
And we according to the question 250 widgets will be delivered i.e. 30 less widgets that the maximum output.
⇒ This 30 can be decreased from C only, because the difference in demand at other locations is 20.
Thus, the number of widgets to be delivered at A , B , C and D will be 70 , 60 , 70 , 50 respectively.
A and C have the highest demand but the distance between W-A is shorter than W-C. so, the first city to visited will be A followed by C.
according to decreasing demand the sequence will be become:
| 1st | 2nd | 3rd | 4th | |
| Warehouse (W) | (A) | (C) | (B) | (D) |
∴ Final Distance (W-A-W-C-B-W-D) = 5 + 5 + 12 + 4 + 10 + 2 = 38km