Comprehension
Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to B, are both short and narrow. In each case, one car takes 6 minutes to cover the distance, and each additional car increases the travel time per car by 3 minutes because of congestion. (For example, if only two cars drive from A to M, each car takes 9 minutes.) On the road from A to N, one car takes 20 minutes, and each additional car increases the travel time per car by 1 minute. On the road from M to B, one car takes 20 minutes, and each additional car increases the travel time per car by 0.9 minute. The police department orders each car to take a particular route in such a manner that it is not possible for any car to reduce its travel time by not following the order, while the other cars are following the order.
Question: 1
How many cars would be asked to take the route A-N-B, that is Akala-Nanur-Bakala route, by the police department?
How many cars would be asked to take the route A-N-B, that is Akala-Nanur-Bakala route, by the police department?
Updated On: Sep 26, 2024
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Correct Answer: 2
Solution and Explanation
Given that there are four cars, and the time through each route is nearly the same, it is recommended to divide the cars into two groups. Two cars should take the route A-M-B, and the other two should take the route A-N-B. If, for some reason, three cars are directed to go through any of the routes, one of the three cars can choose to break the police order and reduce its travel time.
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Question: 2
If all the cars follow the police order, what is the difference in travel time (in minutes) between a car which takes the route A-N-B and a car that takes the route A-M-B?
If all the cars follow the police order, what is the difference in travel time (in minutes) between a car which takes the route A-N-B and a car that takes the route A-M-B?
Updated On: Sep 26, 2024
- 1
- 0.1
- 0.2
- 0.9
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The Correct Option is B
Solution and Explanation
According to the police order, two cars each would pass through A – M – B and A – N – B. The time taken through A – M – B is 29.9, and the time taken through A – N – B is 30.0. Therefore, the difference is 0.1.
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Question: 3
A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and A-M-N-B. On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Assume that any car taking the A-M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the A-N-B route.
How many cars would the police department order to take the A-M-N-B route so that it is not possible for any car to reduce its travel time by not following the order while the other cars follow the order? (Assume that the police department would never order all the cars to take the same route.)
A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and A-M-N-B. On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Assume that any car taking the A-M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the A-N-B route.
How many cars would the police department order to take the A-M-N-B route so that it is not possible for any car to reduce its travel time by not following the order while the other cars follow the order? (Assume that the police department would never order all the cars to take the same route.)
How many cars would the police department order to take the A-M-N-B route so that it is not possible for any car to reduce its travel time by not following the order while the other cars follow the order? (Assume that the police department would never order all the cars to take the same route.)
Updated On: Sep 26, 2024
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Correct Answer: 2
Solution and Explanation
No car should be able to decrease its travel time by disobeying the order, and all cars cannot take the same route. Therefore, either two or three cars should go through A-M. If two cars take the M-B route, one car can violate the police order and opt for M-N, reaching B in 28 minutes compared to the 29.9 minutes required if both had gone through A-M-B. If two cars choose the A-M route and one is directed to go through M-N, one of the cars directed through A-N can violate the police order and go through A-M-B, saving time as follows:
Original time (A-N-B) = 21 + 12 = (three cars) = 33
New time = 12 (three cars) + 20.9 = 32.9
The police department cannot direct both cars to go through M-N, as in that case, all four cars would go through N-B. In case three cars are directed to go through A-M, either one car can be directed through M-N or two cars can be directed through M-N. If one car is directed through M-N, one of the two cars directed through M-B can violate the police order and go through M-N, saving time, as shown.
Original time (A-M-B) = 12 (three cars) + 20.9 = 32.9
New time (A-M-N-B) = 12 + 8 + 12 = 32 minutes.
Therefore, two cars must be directed through M-N to ensure that any car violating the police order cannot reduce the travel time.
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Question: 4
A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and A-M-N-B. On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Assume that any car taking the A-M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the - A-N-B route.
If all the cars follow the police order, what is the minimum travel time (in minutes) from A to B? (Assume that the police department would never order all the cars to take the same route.)
A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and A-M-N-B. On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Assume that any car taking the A-M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the - A-N-B route.
If all the cars follow the police order, what is the minimum travel time (in minutes) from A to B? (Assume that the police department would never order all the cars to take the same route.)
If all the cars follow the police order, what is the minimum travel time (in minutes) from A to B? (Assume that the police department would never order all the cars to take the same route.)
Updated On: Sep 26, 2024
- 26
- 32
- 29.9
- 30
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The Correct Option is B
Solution and Explanation
When all cars follow the police order, the time taken would be:
- A-M-B (1 car) = 12 + 20 = 32 minutes.
- A-M-N-B (2 cars) = 12 + 8 + 12 = 32 minutes.
- A-N-B (1 car) = 20 + 12 = 32 minutes.
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