The average of twelve numbers is 39. The average of the last five numbers is 35, and that of the first four numbers is 40. The fifth number is 6 less than the sixth number and 5 more than the seventh number. The average of the sixth and seventh numbers is:

Solution (By Examveda Team)

Sum of 12 numbers = 12 × 39 = 468
Sum of last 5 numbers = 5 × 35 = 175
Sum of first 4 numbers = 4 × 40 = 160
\[\begin{array}{*{20}{c}} {{5^{{\text{th}}}}}&{{6^{{\text{th}}}}}&{{7^{{\text{th}}}}} \\ {\left( {x - 6} \right)}&{\left( x \right)}&{\left( {x - 11} \right)} \end{array}\]
$$\eqalign{ & 3x - 17 = 468 - \left( {175 + 160} \right) \cr & 3x = 133 + 17 \cr & x = 50 \cr & {\text{Average of }}{{\text{6}}^{{\text{th}}}}{\text{ and }}{{\text{7}}^{{\text{th}}}}{\text{ number}} \cr & = \frac{{x + \left( {x - 11} \right)}}{2} \cr & = x - 5.5 \cr & = 50 - 5.5 \cr & = 44.5 \cr} $$