Jun 132012
 

You have two identical ropes, which are non-uniform in composition. Each rope takes 60 minutes to burn (But non-uniformly, for example: 90% of the rope may burn in 5 min and rest 10% may take 55 min or any such composition). You don’t have any watch but a lighter. How will you calculate 45 minutes?

Solution:

The ropes are non-uniform, it means that if we cut a rope in two halves, then both halves may not take 30 minutes each to burn (But on a whole the rope will take 60 minutes to burn).

To calculate 30 minutes, you only need 1 rope

 - Let the rope from both ends, it will take the rope 30 minutes to burn completely

To calculate 45 minutes, you need 2 ropes, Lets call the ropes A & B. Follow the below process:

 - Burn Rope-A from both ends and Rope-B from one end.
 - Rope-A will completely burn in 30 minutes (because it is put on fire from both ends). 
   when Rope-A is burnt completely, Rope-B would have burnt for 30 minutes (It does not mean that Rope-B is half burnt), 
   At this point lit the other end of Rope-B as well, it will take another 15 minutes for Rope-B to burn completely.

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