The average of thirteen numbers is 47. The average of the first three numbers is 39 and that of next seven numbers is 49. The 11^th number is two times the 12^th number and 12^th number is 3 less than the 13^th number. What is the average of 11^th and 13^th numbers?

Solution (By Examveda Team)

The sum of last three numbers = 47 × 3 + 10 = 151
\[\begin{array}{*{20}{c}} {\,{{11}^{{\text{th}}}}}&{{{12}^{{\text{th}}}}}&{{{13}^{{\text{th}}}}} \\ {2x}&x&{x + 3} \end{array}\]
Sum of 11^th, 12^th and 13^th ;
2x + x + x + 3 = 151
4x + 3 = 151
x = 17
Average of 11^th of 13^th
$$\eqalign{ & = \frac{{2x + x + 3}}{2} \cr & = \frac{{3\left( {x + 1} \right)}}{2} \cr & = 3 \times \frac{{38}}{2} \cr & = 57 \cr} $$