Question 1

Find the maximum distance between A and H if condition is that traveling a city more than once is not allowed.

Accepted Answer

From the solution of question number 25 , Maximum distance is when path taken is: A – D – C – B – G – E – F – H = 1300 + 500 + 200 + 400 + 400 + 300 + 600 = 3700 km. Therefore , the maximum distance between A and H is 3700 km.

Question 2

Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can choose is

Accepted Answer

Map of the town is given as below: It is given that Neelam took the shortest path hence she has to pass through path EF. Number of ways to reach E from A is 2+2C2 = 4C2 = 6. Number of ways to reach B from F is 4+2C2 = 6C2 = 15. Hence total number of ways to reach B from A is 6 x 15 = 90.

Question 3

Neelam rides her bicycle from her house at A to her club at C, via B taking the shortest path. Then the number of possible shortest paths that she can choose is

Accepted Answer

From the answer of previous question, Total number of ways from A to B is 90. Now we need to calculate total number of ways from B to C that is 13 (on the same logic) Hence, total number of paths from A to C is 90 x 13 = 1170.

Question 4

Which of the following is true?

Accepted Answer

As per the given conditions, we require surveillance cameras that would cover all roads converging at an intersection. The cost for covering all the roads has to be minimum. If we put a camera on '1', roads from '7' and '6' to 1 will be covered. If we put a camera on intersection '2', roads converging from '3' to '2' will be covered. If we put a camera on '3', roads from '3' to '5', '6' to '5' and '7' to '5' will be covered. Now we are left with roads from 7 to 4 and from 6 to 4 both of them converge from 4 hence these will be covered by putting a camera on '4'. And then all the roads will be covered and the minimum cost is 2 + 5 + 1 + 4 = 12 lakhs

Question 5

Which nodes should be selected for installation of surveillance cameras?

Accepted Answer

On the basis of above given question ,we can say that Similar to the above answer cameras are put on 2, 5, 1 and 4 to minimize the cost.

Question 6

If a new path is constructed from T7 to Y then find the total number of paths from X to Y?

Accepted Answer

As per the given above diagram , we can see that Total number of paths from X to Y is 7.

Question 7

Which one of the following could be the value of toll taxes at T1, T2, T3…............... T8 such that total cost of travel is same irrespective of route?

Accepted Answer

From the solution of previous question , we have following results: T3 = T7 = 0, T1 = 20 + T2 + T4, T5 = 30 + T6 + T8. From the given options option B satisfies the condition. Hence , required answer will be 50, 20, 0, 10, 60, 20, 0, 10 .

Question 8

What is the difference between maximum amount and minimum amount that Mr. Ricky can spend on a day if he wants to travel from his home (X) to office (Y) if toll tax at each toll booth is Rs 50?

Accepted Answer

On the basis of above given diagram , we can see that Maximum expenditure is in path 3 and that is 260 + 50 x 6 = 260 + 300 = 560 Minimum expenditure is in path 5 and that is 230 + 50 x 3 = 230 + 150 = 380 ∴ Required difference = Maximum expenditure is in path 3 - Minimum expenditure is in path 5 = 560 – 380 = 180 Hence , Required difference is 180.

Question 9

If toll tax is devised in such a way that total cost of travel remains same irrespective of the path then what is the minimum cost of travel from X to Y?

Accepted Answer

From the given condition , cost incurred in path 2 is equal to that in path 3 then T3 = 0 Similarly ,equating cost of path 3 and path 4 T7 = 0 Equating cost of path 4 and path 5 we will get 260 + T6 + T8 = 230 + T5 ⇒ T5 = T6 + T8 + 30 Equating cost of path 1 and path 2 we will get , 240 +T1 = 260 + T2+ T4 or T1 = T2 + T4 + 20 For minimum total cost T1 = 20 and T5 = 30 then cost incurred is Rs 260. Therefore , the minimum cost of travel from X to Y is Rs 260 .

Question 10

If toll tax at all of the toll booths is same and is devised such that the ratio of maximum cost to minimum cost of travel from X to Y is 28 : 19 then which one of the following is the cost of travel from X to Y through toll Both T3?

Accepted Answer

If toll tax at all of the toll booths is same and let it be k then expense in each path is as follows: Path 1: 240 + 3k Path 2: 260 + 5k Path 3: 260 + 6k Path 4: 260 + 5k Path 5: 230 + 3k So from the given condition On solving we will get k = 50 Tool booth 3 will come in Path 3 and Path 4. So cost incurred is: Path 3: 260 + 6k = 260 + 300 = 560 Path 4: 260 + 5k = 260 + 250 = 510 Therefore , 560 or 510 is the cost of travel from X to Y through toll Both T3 .

Question 11

For a route that satisfies the above restrictions, which of the following statements is true?

Accepted Answer

According to question , Here ,we will eliminate the options one by one. Option (A) cannot be true as there are many routes that satisfy the given condition. Option (C) is also not true as we can have a route starting from D (e.g. DEBDCBAC). The route need not necessarily end at E, which is apparent. Option B satisfies all the conditions. Hence , A route can either start at C or end at C, but not both.

Question 12

How many different starting cities are possible such that the above restriction is satisfied?

Accepted Answer

On the basis of above given figure , we can see that City A is connected by 2 roads, B by 4 roads, C by 3 roads, D by 3 roads and E by 2 roads. For a city to be starting city for such a route, it has to be connected by odd number of roads. Hence the required answer is 2, i.e. C and D.

Question 13

What is the distance between A and B?

Accepted Answer

As per the above result , Route -1 :- 5 + AB = 13 ⇒ AB = 13 - 5 = 8 km Hence , required distance between A and B is 8 km .

Question 14

What is the length of route - 2 ?

Accepted Answer

From the above result length of route -2 = 11 km Therefore , the length of route -2 is 11 km .

Question 15

What is the number of routes from P to Q?

Accepted Answer

As per the given above figure , we can see that The number of routes from P to Q = 2 + 4 = 6 Hence , the number of routes from P to Q is 6 .

Routes and Networks Questions