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 ✓ UPSC's answer
- (b) 22 minutes
- (c) 21 minutes
- (d) 20 minutes
Why the answer is (a)
• The rule that the faster person of each pair returns with the lamp 'to accompany another person' means A (1 minute), the fastest, escorts each of the others across and brings the lamp back.
• A and D cross (10 min), A returns (1); A and C cross (7), A returns (1); A and B cross (2) — everyone is across in 21 minutes.
• The lamp must then be returned to the original place (A walks back, 1 min) and A crosses again without the lamp (1 min).
• Total = 21 + 1 + 1 = 23 minutes.
• Hence 23 minutes, option (a), as in the official key.
Why the other options are wrong
- (b) 22 minutes
- The escort sequence gives 21 minutes plus 2 for returning the lamp and recrossing = 23, not 22.
- (c) 21 minutes
- 21 minutes gets everyone across but omits returning the lamp and recrossing.
- (d) 20 minutes
- 20 minutes is less than the time the stated rules require.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.