Set 2 : Cars Travel Route
Q1-4. 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.
1. How many cars would be asked to take the route A-N-B, that is Akala-Nanur-Bakala route, by the police department? (TITA)
EXPLANATION
Answer: 2
A-M-B and A-N-B routes and the time taken for each narrow and broad roads are given in the below pictures. Based on those pictures, we can solve the questions.
When 2 cars were sent in the both routes, the time is minimal for both routes.
Hence, the answer is “2”.
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?
- 1
- 0.1
- 0.2
- 0.9
EXPLANATION
Answer: 0.1
A-M-B and A-N-B routes and the time taken for each narrow and broad roads are given in the below pictures. Based on those pictures, we can solve the questions.
When 2 cars were sent in the both routes, the time is minimal for both routes.
In that case, the difference = 30 – 29.9 = 0.1
Hence, the answer is “0.1”.
Choice 2 is the correct answer.
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.) (TITA)
EXPLANATION
Answer: 2
A-M-B and A-N-B routes and the time taken for each narrow and broad roads are given in the below pictures. Based on those pictures, we can solve the questions.
When 1, 2, 1 cars were sent in the A-M-B, A-M-N-B, A-N-B routes, the time is minimal for all three routes.
Hence, the answer is “2”.
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.)
- 26
- 32
- 29.9
- 30
EXPLANATION
Answer: 32
A-M-B and A-N-B routes and the time taken for each narrow and broad roads are given in the below pictures. Based on those pictures, we can solve the questions.
When 1, 2, 1 cars were sent in the A-M-B, A-M-N-B, A-N-B routes, the time is minimal for all three routes.
In that case, the minimum time is 32 minutes.
Hence, the answer is “32”.
Choice B is the correct answer.
