Burning Ropes with Time Measurement

Problem : There is this special kind of ropes made from some non-homogeneous material. Because of this special material, the rope takes exactly one hour to burn if lighted from one end. However, as the material is not uniform across the rope, different parts of rope may take different amount of time. So for example, one half may take 1 minute where as other half may take 59 minutes to burn.

you are given two such ropes  and you need to measure

1. 1hr

2. 45 minute

3. 30 minute

4. 15 minute

Solution

1. If we burn a single rope then we can measure 1 hr.

2. Burning of two ends of it at the same let you you measure 30 minutes.

3. Now start by lighting both ends of one rope and one end of other rope. when first rope is finished burning(in 30 minutes) then light other end of second rope ,in this way second rope half second rope is already burned so it will take more 15 minutes with both ends burning. so you can measure 45 minutes.

4.  When second rope is done burning then already 45 minutes has elapsed. 15 minutes has elapsed after first rope has completely burnt. so you can measure 15 minutes in this case.