The average of 11 numbers is 63. If the average of first six numbers is 60 and the last six numbers is 65, then the 6th number is

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