Four friends A, B, C and D need to cross a bridge. A maximum of 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:

Correct Option (1)

The objective is to determine the minimum time for all four friends (A, B, C, D) to cross the bridge, adhering to the specified conditions. The individual crossing times are A: 1 minute, B: 2 minutes, C: 7 minutes, D: 10 minutes. A maximum of two persons can cross at a time, carrying a single lamp, and a pair moves at the speed of the slower person. The faster person returns with the lamp.

A systematic approach to minimize total time involves the fastest person (A) repeatedly ferrying others across and returning with the lamp. The sequence of crossings and returns is as follows:

• First Crossing: Persons A and B cross the bridge. The time taken is determined by the slower person, B, which is 2 minutes. Person A then returns with the lamp, taking 1 minute. Total time for this step: 2 minutes (A+B cross) + 1 minute (A returns) = 3 minutes.
• Second Crossing: Persons A and C cross the bridge. The time taken is determined by C, which is 7 minutes. Person A then returns with the lamp, taking 1 minute. Total time for this step: 7 minutes (A+C cross) + 1 minute (A returns) = 8 minutes.
• Third Crossing: Persons A and D cross the bridge. The time taken is determined by D, which is 10 minutes. Person A then returns with the lamp, taking 1 minute. Total time for this step: 10 minutes (A+D cross) + 1 minute (A returns) = 11 minutes.
• Final Crossing: Person A crosses the bridge alone to join the others. This takes 1 minute. Total time for this step: 1 minute.

The total minimum time required is the sum of the times for each step: 3 minutes + 8 minutes + 11 minutes + 1 minute = 23 minutes.

Incorrect Options:

Options 2, 3, and 4 present values (22, 21, 20 minutes) that are less than the calculated minimum time of 23 minutes using the described optimal strategy. Therefore, these options do not represent the correct minimum time required for all friends to cross the bridge under the given conditions.