Q6 BT: Burning Ropes

Question 6 from the book “A Practical Guide to Quantitative Finance Interviews” by Zhou Xinfeg.

You have two ropes, each of which takes I hour to burn. But either rope has different densities at different points, so there’s no guarantee of consistency in the time it takes different sections within the rope to bum. How do you use these two ropes to measure 45 minutes?

Solution and explanation

Get one of the ropes and burn it at either end and the second one end. It will take 30 minutes to burn up the first one. At this instance the second will still be left with 30 minutes to burn out. Immediately burn the other end of the second rope. This will halve the 30 minutes left to 15. Add 15 for this last half of the second rope to 30 for burning the first rope and half one of the second rope and you have 45 minutes.

That’s it for this one.