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 : 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?a)23 minutesb)22 minutesc)21 minutesd)20 minutesCorrect answer is option 'A'. Can you explain this answer?

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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 : 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?

a)
23 minutes
b)
22 minutes
c)
21 minutes
d)
20 minutes

Correct answer is option 'A'. Can you explain this answer?

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

Here, A takes the shortest time to cross the bridge i.e. 1 min. And, D takes 10 min, C takes 7 min and B takes 2 min to cross the bridge.

So 4 friends can cross the bridge in minimum time in the following way:

A + B crossing and A returning : (2 + 1) min = 3 min

A + C crossing and A returning : (7 + 1) min = 8 min

A + D crossing and A returning : (10 + 1) min = 11 min

A crossing the bridge for the last time: 1 min

Hence, total minimum time = 3 + 8 + 11 + 1 = 23 min.

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Most Upvoted Answer

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

To find the minimum time required by all the friends to cross the bridge, we need to analyze the different combinations of pairs crossing the bridge. Let's consider the possible combinations:

1. A and B cross the bridge: Total time = 2 minutes
- B returns with the lamp: Total time = 2 + 2 = 4 minutes
2. A and C cross the bridge: Total time = 7 minutes
- A returns with the lamp: Total time = 7 + 1 = 8 minutes
3. A and D cross the bridge: Total time = 10 minutes
- A returns with the lamp: Total time = 10 + 1 = 11 minutes
4. B and C cross the bridge: Total time = 7 minutes
- B returns with the lamp: Total time = 7 + 2 = 9 minutes
5. B and D cross the bridge: Total time = 10 minutes
- B returns with the lamp: Total time = 10 + 2 = 12 minutes
6. C and D cross the bridge: Total time = 10 minutes
- C returns with the lamp: Total time = 10 + 7 = 17 minutes

From the above combinations, we can see that the minimum time is achieved when A and B cross the bridge first, followed by A returning with the lamp, and then C and D crossing the bridge. Finally, B and A cross the bridge together without the lamp.

So, the total minimum time required by all the friends to cross the bridge is 2 + 2 + 7 + 1 + 2 = 14 minutes. However, we need to add the time taken by A to return without the lamp, which is 1 minute.

Therefore, the total minimum time required by all the friends to cross the bridge is 14 + 1 = 15 minutes.

None of the options provided in the question matches this answer. Hence, the given options are incorrect.

However, if we analyze the combinations further, we can find a better solution:

1. A and B cross the bridge: Total time = 2 minutes
- B returns with the lamp: Total time = 2 + 2 = 4 minutes
2. A returns with the lamp: Total time = 4 + 1 = 5 minutes
3. C and D cross the bridge: Total time = 10 minutes
- A gives the lamp to C: Total time = 10 + 7 = 17 minutes
4. A and B cross the bridge without the lamp: Total time = 2 minutes

Therefore, the total minimum time required by all the friends to cross the bridge is 2 + 4 + 5 + 10 + 7 + 2 = 30 minutes.

Again, none of the options provided in the question matches this answer.

Considering the given options, the closest answer is option 'A' (23 minutes) if we assume that the time taken by the person returning without the lamp is not counted. However, this contradicts the problem statement, which states that the person returning without the lamp must cross the bridge again.

Answered by Notes Wala · View profile

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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 : 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?a)23 minutesb)22 minutesc)21 minutesd)20 minutesCorrect answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 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 : 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?a)23 minutesb)22 minutesc)21 minutesd)20 minutesCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 : 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?a)23 minutesb)22 minutesc)21 minutesd)20 minutesCorrect answer is option 'A'. Can you explain this answer?.

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