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- Question
- If the government wants to ensure that no traffic flows on the street from D to T, while equal amount of traffic flows through junctions A and C, then a feasible set of toll charged (in rupees) at junctions A, B, C and D respectively to achieve this goal is
Options- A. 1, 5, 3, 3
- B. 1, 4, 4, 3
- C. 1, 5, 4, 2
- D. 0, 5, 2, 3
- Correct Answer
-
ExplanationFrom the given diagram ,
Let the toll charged at junctions A, B, C and D be a, b, c and d respectively.
Then 1st we will list down all the routes and corresponding cost of travel.
Since the cost of travel including toll on routes S-A-T, S-B-C-T, S-B-A-T and S-D-C-T is the same. And D-T has no traffic due to high toll charge at D.
From the last solutions we will get b = 5, 14 + a = 7 + b + c = 12 + c, or a + 2 = c 7 + b + c = 10 + c + d = 12 + c or d = 2, hence the result is B = 5, d = 2 and c-a = 2 that is satisfied by option (E). - 1. If the government wants to ensure that the traffic at S gets evenly distributed along streets from S to A, from S to B, and from S to D, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:
Options- A. 0, 5, 4, 1
- B. 0, 5, 2, 2
- C. 1, 5, 3, 3
- D. 1, 5, 3, 2 Discuss
- 2. The government wants to devise a toll policy such that the total cost to the commuters per trip is minimized. The policy should also ensure that not more than 70 percent of the total traffic passes through junction B. The cost incurred by the commuter travelling from point S to point T under this policy will be:
Options- A. $ 7
- B. $ 9
- C. $ 10
- D. $ 13 Discuss
- 3. If the government wants to ensure that all routes from S to T get the same amount of traffic, then a feasible set of toll charged (in rupees) at junctions A, B, C and D respectively to achieve this goal is :
Options- A. 0, 5, 2, 2
- B. 0, 5, 4, 1
- C. 1, 5, 3, 3
- D. 1, 5, 3, 2 Discuss
- 4. If the government wants to ensure that all motorists travelling from S to T pay the same amount ( fuel costs and toll combined ) regardless of the route they choose and the street from B to C is under repairs ( and hence unusable ), then a feasible set of toll charged (in rupees) at junctions A, B, C and D respectively to achieve this goal is :
Options- A. 2, 5, 3, 2
- B. 0, 5, 3, 1
- C. 1, 5, 3, 2
- D. 2, 3, 5, 1 Discuss
- 5. In the adjoining figure, the lines represent one-way roads allowing travel only northwards or only westwards. Along how many distinct routes can a car reach point B from point A?
Options- A. 15
- B. 56
- C. 120
- D. 336 Discuss
- 6. Find the ratio of maximum to minimum distance between A and H if condition is that traveling a city more than once is not allowed.
Options- A. 37 : 14
- B. 37 : 23
- C. 39 : 14
- D. None of these Discuss
- 7. Find the total number of paths from city H to city A if condition is that traveling a city more than once is not allowed.
Options- A. 44
- B. 55
- C. 59
- D. None of these Discuss
- 8. Find the minimum distance between H to A without visiting city E.
Options- A. 1200
- B. 1300
- C. 1400
- D. None of these Discuss
- 9. What is the minimum distance between H to A through D?
Options- A. 1800
- B. 2000
- C. 2200
- D. None of these Discuss
- 10. If path H E C is taken and no city is visited twice then find the total number of such paths.
Options- A. 3
- B. 4
- C. 5
- D. None of these Discuss
Routes and Networks problems
Search Results
Correct Answer: 0, 5, 4, 1
Explanation:
According to question ,
If all the five routes have the same cost, then there will be an equal flow in all the five routes, i.e. 20% in each route.
But then the percentage of traffic in S - A = 20% (Only one route involving S - A)
S - B = 40% (As there are two routes involving S - B)
S - D = 40% (As there are two routes involving S - D)
But here the given condition that traffic in S-A is equal to that in S - B, which in turn is equal to S - D is not satisfied.
Of the routes, that can be used the number of routes involving S - A must be the same as S - B, which in turn is same as that as S - D.
That is possible only when we block the junction C and that can be done by taking higher toll charge at C to achieve this goal c > 3.
Hence , required answer will be option A .
Correct Answer: $ 10
Explanation:
On the basis of above given question , we can say that
There must be one other route other than those involving B.
We must take S - D - C - T as the other route.
S - B - C - T, if toll at B = 3, total cost = 10
S - D - C - T, if toll at D and C is 0, total cost is 10.
Hence ,$ 10 is the least cost.
Correct Answer: 1, 5, 3, 2
Explanation:
As per the given diagram , we can see that
Let the toll charged at junctions A, B, C and D be a, b, c and d respectively.
Then 1st we will list down all the routes and corresponding cost of travel.
Here in this case all 5 routes have the same toll charge hence 14 + a = 7 + b + c = 13 + d = 9 + a + b = 10 + c + d
After solving we will get a = 1, b = 5, c = 3 and d = 2
Correct Answer:
Explanation:
As per the given figure , we can see that
Let the toll charged at junctions A, B, C and D be a, b, c and d respectively.
Then 1st we will list down all the routes and corresponding cost of travel.
Since Route BC is under repair hence route S-B-C-T is not in use.
Rest all four have the same toll charges hence 14 + a = 9 + a + b ? b = 14 - 9 = 5
Similarly 10 + c + d = 13 + d ? c = 13 - 10 = 3
Hence Options 4 is ruled out, now if we check option rest 3 options we will find out that option 2 and 3 both are correct. Option (2)/(3) Inconsistent options .
Correct Answer: 56
Explanation:
Here , number of vertical steps ( v ) = 3
Number of horizontal steps ( h ) = 5
Then in this case total number of ways is given by h+vCh = h+vCv = 8C3 = 6 x 7 x ( 8/6 ) = 7 x 8 = 56.
Hence , 56 distinct routes can a car reach point B from point A .
Correct Answer: 37 : 14
Explanation:
From the above given diagram , we can see that
Maximum distance is when path taken is-
A ? D ? C ? B ? G ? E ? F ? H = 1300 + 500 + 200 + 400 + 400 + 300 + 600 = 3700 km
Minimum distance is when path taken is-
A ? C ? G ? H = 600 + 400 + 400 = 1400 km
Hence , Required ratio is 37 : 14.
Correct Answer: 55
Explanation:
Number of paths is as follows:
Starting from HGB: HGBA, HGBCA, HGBCDA, HGBCEDA, HGBCEFDA (Total 5 paths)
Starting from HGC: HGCA, HGCBA, HGCDA, HGCEDA, HGCEFDA (Total 5 paths)
Starting from HGE: HGECA, HGECBA, HGECDA, HGEDCA, HGEDCBA, HGEDA, HGEFDCBA, HGEFDCA, HGEFDA (Total 9 paths)
Starting from HEG: HEGBA, HEGCBA, HEGCA, HEGCDA (Total 4 paths)
Starting from HEC: HECGBA, HECBA, HECA, HECDA (Total 4 paths) Starting from HED: HEDCBGA, HEDCBA, HEDCA, HEDA (Total 4 paths)
Starting from HEF: HEFDCGBA, HEFDCBA, HEFDCBA, HEFDCA, HEFDA (Total 5 paths)
Starting from HFE: HFEGBA, HFECGBA, HFECBA, HFECA, HFEDCGBA, HFEDCBA, HFEDCA, HFEDA, (Total 8 paths)
Starting from HFD: HFDEGBA, HFDEGCA, HFDEGBCA, HFDECGBA, HFDECBA, HFDECA, HFDCEBGA, HFDCGBA, HFDCBA, HFDCA, HFDA (Total 11 paths)
Total number of paths is: 5 + 5 + 9 + 4 + 4 + 4 + 5 + 8 + 11 = 55
Hence , the total number of paths from city H to city A is 55 .
Correct Answer: 1400
Explanation:
As per the given above diagram , we can see that
For minimum distance path is HGCA = 400 + 400 + 600 = 1400
Therefore , the minimum distance between H to A without visiting city E is 1400 km .
Correct Answer: None of these
Explanation:
On the basis of above given diagram , we can say that
The minimum distance between A and H through D is HEDCA and distance is 500 + 500 + 500 + 600 = 2100.
Hence , required answer will be 2100 km.
Correct Answer: 4
Explanation:
From solution of question number 26 ,
Starting from HEC: HECGBA, HECBA, HECA, HECDA (Total 4 paths)
Hence , the total number of such paths is 4 .
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