I have 2 hour glass one measures 11 minute and another measures 7 minute. how u measure 15 minutes? using only one flip of any one of hour glass.

Let us again make use of the a rel='nofollow' href="https://www.cut-the-knot.org/blue/Euclid.shtml#important"identity/abr /a·X - b·Y = 1br /Let a = 11 and b = 7. It's immediately verified that the identity is satisfied by X = 2 and Y = 3. This suggests the following strategy:br /emStart both glasses. When they become successively empty, turn the small glass, then the big one and the small one again. On its third run the small glass will empty 21 minutes from the start of the experiment. Start boiling your eggs at this point but do not yet turn the 7 min glass. After 1 minute (22 minutes after the beginning of the experiment) the big hourglass will become empty. Now, use the small glass twice to count 14 minutes. 1 + 14 = 15. In all, it will take 4 turns for the small glass and 1 turn for the bigger one./em