IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Logical Reasoning · Question 15

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Quant Based Puzzles and Optimisation, with the answer and a step-by-step solution.

Quant Based Puzzles and OptimisationLOGICAL REASONING - High LevelMultiple choiceMedium
Four people must cross a narrow bridge at night. They have one torch between them, the bridge takes at most two people at a time, and anyone crossing must carry the torch. Walking alone they need 1, 2, 5 and 10 minutes respectively, and a pair crosses at the slower person's pace. What is the least total time in which all four can get across?
  1. A
    17 minutes
  2. B
    15 minutes
  3. C
    19 minutes
  4. D
    21 minutes
Pick an option, then check.
Answer & solution

Answer: Option A

The obvious plan is to let the fastest person ferry the torch back each time: 1 and 2 cross, 1 returns, 1 and 5 cross, 1 returns, 1 and 10 cross. That takes 2 + 1 + 5 + 1 + 10 = 19 minutes.

It can be beaten, because the two slowest should cross together so that the 10 and the 5 are paid for in a single trip.

1 and 2 cross together, which takes 2 minutes.

1 comes back with the torch, which takes 1 minute, bringing the total to 3.

5 and 10 cross together, which takes 10 minutes, bringing the total to 13.

2 comes back with the torch, which takes 2 minutes, bringing the total to 15.

1 and 2 cross together, which takes 2 minutes, bringing the total to 17.

All four are across in 17 minutes, and no plan does better.

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