Four friends A, B, C and D need to cross a bridge. A maximum two persons can cross it at a time. It is night and they just have one lamp. Persons that cross the bridge must carry the lamp to find the way. A pair must walk together at the speed of slower person. After crossing the bridge, the person having faster speed in the pair will return with the lamp each time to accompany another person in the group. Finally, the lamp has to be returned at the original place and the person who returns the lamp has to cross the bridge again without lamp. To cross the bridge, the time taken by them is as follows: A :1 minute, B : 2 minutes, C : 7 minutes and D : 10 minutes. What is the total minimum time required by all the friends to cross the bridge?
Four friends A, B, C and D need to cross a bridge. A maximum two persons can cross it at a time. It is night and they just have one lamp. Persons that cross the bridge must carry the lamp to find the way. A pair must walk together at the speed of slower person. After crossing the bridge, the person having faster speed in the pair will return with the lamp each time to accompany another person in the group. Finally, the lamp has to be returned at the original place and the person who returns the lamp has to cross the bridge again without lamp. To cross the bridge, the time taken by them is as follows: A :1 minute, B : 2 minutes, C : 7 minutes and D : 10 minutes. What is the total minimum time required by all the friends to cross the bridge? Correct Answer 23 minutes
Time taken by different people to cross the bridge:
A = 1 minute
B = 2 minutes
C = 7 minutes
D = 10 minutes
The person who will accompany other persons to cross the bridge has to be the fastest so that they can save time while returning.
Fastest Person is A. Therefore,
First A and B will go, which will take them 2 minutes to cross the bridge. Then A will return in 1 minute. Total = 3 minutes
Then, A and C will go, which will take them 7 minutes. Then A will return in 1 minute. Total = 8 minutes
Then, A and D will go, which will take them 10 minutes. Then A will return in 1 minute. Total = 11 minutes
Finally, A will cross the bridge alone in 1 minute.
Total time = 3 + 8 + 11 + 1 = 23 minutes
Hence, a minimum of 23 minutes is required for all of them to cross the bridge.