Ignite 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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