QUESTION

CSAT

Hard

Maths

Prelims 2016

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 the 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 the 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?

Select an option to attempt

Explanation

A and B cross the bridge together, taking 2 minutes (since the time taken by the slower person is considered).

A then returns with the lamp, taking 1 minute. Total time after this step = 22 (crossing) + 11 (returning) = 33 minutes. C and D cross together, taking 10 minutes (since the time taken by the slower person is considered).

B returns with the lamp, taking 2 minutes. Total time after this step = 33 (previous total) + 1010 (crossing) + 22 (returning) = 1515 minutes. A and B cross again together, taking 2 minutes.

Total time after this step = 1515 (previous total) + 22 (crossing) = 1717 minutes. The total minimum time required for all the friends to cross the bridge is 23 minutes.

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