Explanation
The individual crossing times for the four friends are:
A=1 minute
B=2 minutes
C=8 minutes
D=11 minutes
To minimize the total crossing time, the key strategy is to ensure that the two slowest people (C and D) cross together so that their slow times overlap, and a fast mover is on the other side to bring the lamp back.
Let's break down the optimal sequence of steps:
Step Number | Action | People Crossing | Time Taken | Remaining on Starting Side | Reached the Destination Side |
|---|
Step 1 | A and B cross the bridge with the lamp. | A,B→ | max(1,2)=2 mins | C,D | A,B |
Step 2 | A returns with the lamp to the starting side. | ←A | 1 min | A,C,D | B |
Step 3 | The two slowest people, C and D, cross together. | C,D→ | max(8,11)=11 mins | A | B,C,D |
Step 4 | B (who was waiting) returns with the lamp. | ←B | 2 mins | A,B | C,D |
Step 5 | Finally, A and B cross the bridge together. | A,B→ | max(1,2)=2 mins | None | A,B,C,D |
Total Time Calculation
Now, sum up the time taken in each individual step:
Total Time=Step 1+Step 2+Step 3+Step 4+Step 5
Total Time=2+1+11+2+2
Total Time=18 minutes
Correct Answer: C) 18 minutes
