Let the 11 numbers be $$N_{1}$$, $$N_{2}$$, $$N_{3}$$.......$$N_{11}$$ Average of 11 numbers = 63 => $$N_{1}$$ + $$N_{2}$$ + $$N_{3}$$+.......+$$N_{11}$$ = 63*11 = 693 -----------Eqn{1} Average of first 6 = 60 => $$N_{1}$$ + $$N_{2}$$+...+$$N_{6}$$ = 60*6 = 360 -----------Eqn {2} Average of last 6 = 65 => $$N_{6}$$ + $$N_{7}$$+....+$$N_{11}$$ = 65*6 = 390 ----------Eqn{3} Adding eqn 2 and 3, we get $$N_{1}$$ + $$N_{2}$$+...+2*$$N_{6}$$+....+$$N_{11}$$ = 360+390 = 750 Subtracting eqn 1 from it, we will be left with => $$N_{6}$$ = 750-693 = 57