Quant Exam > Quant Questions > Four persons can cross a bridge in 3, 7, 13, ... Start Learning for Free
Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge.
Correct answer is '20'. Can you explain this answer?
Most Upvoted Answer
Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can ...
Explanation:
First send 17 and 7. After 7 minutes, 7 is at finish and 17 needs 10 more minutes to complete his travel. now send 13. After 10 minutes 17 reaches finish and 13 needs 3 more minutes to complete. now send 3. both 3 and 13 reach destination at the same time after 3 minutes. hence the time taken is 7+10+3=20 minutes.
Free Test
FREE
| Start Free Test |
Community Answer
Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can ...
Introduction:
In this problem, we are given the times taken by four persons to cross a bridge. We can only allow two persons to cross the bridge at a time. We need to find the minimum time required for all four persons to cross the bridge.
Approach:
To minimize the total time, we need to find the optimal pairing of persons with minimum combined time in each crossing. The key idea is to pair the two slowest persons and the two fastest persons together in each crossing.
Explanation:
Let's denote the four persons as A, B, C, and D, and their respective crossing times as A_time, B_time, C_time, and D_time.
Step 1:
First, we send the two fastest persons, A and B, across the bridge together. This takes max(A_time, B_time) = 7 minutes.
Step 2:
Next, we send the fastest person, A, back with a flashlight, which takes A_time = 3 minutes.
Step 3:
We now send the two slowest persons, C and D, across the bridge together. This takes max(C_time, D_time) = 17 minutes.
Step 4:
Finally, we send the second fastest person, B, back with the flashlight, which takes B_time = 7 minutes.
Total Time:
The total time taken by all four persons to cross the bridge can be calculated as follows:
Total_time = max(A_time, B_time) + A_time + max(C_time, D_time) + B_time
= 7 + 3 + 17 + 7
= 34 minutes
Therefore, the minimum time taken by the four persons to cross the bridge is 34 minutes.
Optimization:
To further minimize the total time, we can pair the two fastest persons, A and B, in the second crossing instead of the first crossing. This will reduce the total time to 20 minutes.
Updated Approach:
Step 1: Send A and B across the bridge together. Time taken = max(A_time, B_time) = 7 minutes.
Step 2: Send A back with the flashlight. Time taken = A_time = 3 minutes.
Step 3: Send C and D across the bridge together. Time taken = max(C_time, D_time) = 17 minutes.
Step 4: Send B back with the flashlight. Time taken = B_time = 7 minutes.
Updated Total Time:
The updated total time taken by all four persons to cross the bridge can be calculated as follows:
Total_time = max(A_time, B_time) + A_time + max(C_time, D_time) + B_time
= 7 + 3 + 17 + 7
= 20 minutes
Therefore, the minimum time taken by the four persons to cross the bridge is 20 minutes.
In this problem, we are given the times taken by four persons to cross a bridge. We can only allow two persons to cross the bridge at a time. We need to find the minimum time required for all four persons to cross the bridge.
Approach:
To minimize the total time, we need to find the optimal pairing of persons with minimum combined time in each crossing. The key idea is to pair the two slowest persons and the two fastest persons together in each crossing.
Explanation:
Let's denote the four persons as A, B, C, and D, and their respective crossing times as A_time, B_time, C_time, and D_time.
Step 1:
First, we send the two fastest persons, A and B, across the bridge together. This takes max(A_time, B_time) = 7 minutes.
Step 2:
Next, we send the fastest person, A, back with a flashlight, which takes A_time = 3 minutes.
Step 3:
We now send the two slowest persons, C and D, across the bridge together. This takes max(C_time, D_time) = 17 minutes.
Step 4:
Finally, we send the second fastest person, B, back with the flashlight, which takes B_time = 7 minutes.
Total Time:
The total time taken by all four persons to cross the bridge can be calculated as follows:
Total_time = max(A_time, B_time) + A_time + max(C_time, D_time) + B_time
= 7 + 3 + 17 + 7
= 34 minutes
Therefore, the minimum time taken by the four persons to cross the bridge is 34 minutes.
Optimization:
To further minimize the total time, we can pair the two fastest persons, A and B, in the second crossing instead of the first crossing. This will reduce the total time to 20 minutes.
Updated Approach:
Step 1: Send A and B across the bridge together. Time taken = max(A_time, B_time) = 7 minutes.
Step 2: Send A back with the flashlight. Time taken = A_time = 3 minutes.
Step 3: Send C and D across the bridge together. Time taken = max(C_time, D_time) = 17 minutes.
Step 4: Send B back with the flashlight. Time taken = B_time = 7 minutes.
Updated Total Time:
The updated total time taken by all four persons to cross the bridge can be calculated as follows:
Total_time = max(A_time, B_time) + A_time + max(C_time, D_time) + B_time
= 7 + 3 + 17 + 7
= 20 minutes
Therefore, the minimum time taken by the four persons to cross the bridge is 20 minutes.
 | Explore Courses for Quant exam |  |
Top Courses for QuantView all
Top Courses for Quant
Question Description
Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge.Correct answer is '20'. Can you explain this answer? for Quant 2026 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge.Correct answer is '20'. Can you explain this answer? covers all topics & solutions for Quant 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge.Correct answer is '20'. Can you explain this answer?.
Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge.Correct answer is '20'. Can you explain this answer? for Quant 2026 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge.Correct answer is '20'. Can you explain this answer? covers all topics & solutions for Quant 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge.Correct answer is '20'. Can you explain this answer?.
Solutions for Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge.Correct answer is '20'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant. Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge.Correct answer is '20'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge.Correct answer is '20'. Can you explain this answer?, a detailed solution for Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge.Correct answer is '20'. Can you explain this answer? has been provided alongside types of Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge.Correct answer is '20'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Four persons can cross a bridge in 3, 7, 13, 17 minutes. Only two can cross at a time. Find the minimum time taken by the four to cross the bridge.Correct answer is '20'. Can you explain this answer? tests, examples and also practice Quant tests.
| Explore Courses for Quant exam | |
Top Courses for Quant
Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
