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Four friends A, B, C and D need to cross a bridge in the night. A maximum of 2 people can cross at a time. They have only one lamp. A takes one minute to cross the bridge. B takes 2 minutes, C takes 8 minutes and D takes 11 minutes to cross the bridge respectively. A pair must walk together at the speed of the person who walks slowly. What is the minimum time required to cross the bridge by all four people? 

Four friends A, B, C and D need to cross a bridge in the night. A maximum of 2 people can cross at a time. They have only one lamp. A takes one minute to cross the bridge. B takes 2 minutes, C takes 8 minutes and D takes 11 minutes to cross the bridge respectively. A pair must walk together at the speed of the person who walks slowly. What is the minimum time required to cross the bridge by all four people?  Correct Answer 23 minutes

Friends

Time taken to cross bridge

A

1 minute

B

2 minutes

C

8 minutes

D

11 minutes

A pair must walk together at the speed of the person who walks slowly.

As A takes the shortest time, so each friend will walk with A.

Time taken:

A crossing the bridge with B and then retuning = 1 + 2 minutes

= 3 minutes

A crossing the bridge with C and then retuning = 1 + 8 minutes

= 9 minutes

A crossing the bridge with D = 11 minutes

A won’t return as none of the friend is left.

So, the minimum time required to cross the bridge by all the four people = (3 + 9 + 11) minute

= 23 minutes

Hence, ’23 minutes’ is the correct answer.

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