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?
Answer & explanation
Answer: (a) 23 minutes
Because the faster member of each pair must bring the lamp back, A (1 minute) should escort each of the others: 10 + 1 + 7 + 1 + 2 = 21 minutes. Taking the lamp back and crossing again without it adds A's 1 + 1 minutes, giving 23.
- The faster person of each pair returns with the lamp, so the fastest, A, should pair with each of the others.
- A and D cross: 10 min; A returns: 1 min.
- A and C cross: 7 min; A returns: 1 min.
- A and B cross: 2 min. All are across after 10 + 1 + 7 + 1 + 2 = 21 min.
- A takes the lamp back (1 min) and crosses again without it (1 min): 21 + 2 = 23 minutes.
- Check: any pair without A sends back B or slower, which only adds time.
Remember · Read the special rules first: here the faster partner must return, so the fastest person should shuttle everyone.
Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·