UPSC Prelims 2016 · CSAT
Question 27: Logical Reasoning and Mental Ability
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 ?
AnswerUPSC’s answer is (a).
The rule makes the faster person of each crossing pair bring the lamp back, so A (1 min) does all the shuttling. A and B cross: 2; A returns: 1; A and C cross: 7; A returns: 1; A and D cross: 10. That is 21 so far. The lamp must then go back to the start (A returns, 1 min) and A crosses again without the lamp (1 min). Total = 2 + 1 + 7 + 1 + 10 + 1 + 1 = 23. The well-known 17-minute plan breaks this rule.
Why each option is right or wrong
- (a) Right: 2 + 1 + 7 + 1 + 10 + 1 + 1 = 23 under the stated rule.
- (b) Not reachable while the faster person of each pair must carry the lamp back.
- (c) Not reachable under the stated rule.
- (d) Not reachable under the stated rule; it needs the cheaper plan the rule forbids.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2016, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.