If the average of 5 consecutive integers is x then, find the average of next to next 5 consecutive integers.

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let numbers be }}a,\,a + 1,\,a + 2,\,a + 3,\,a + 4 \cr & {\text{Next, }}a + 5,\,a + 6,\,a + 7,\,a + 8,\,a + 9 \cr & {\text{Next to Next, }}a + 10,\,a + 11,\,a + 12,\,a + 13,\,a + 14 \cr & {{\text{I}}^{{\text{st}}}}{\text{ condition}} = \frac{{5a + 10}}{5} = x \cr & 5a + 10 = 5x\,......\,\left( {\text{i}} \right) \cr & {\text{I}}{{\text{I}}^{{\text{nd}}}}{\text{ condition}} \cr & = \frac{{a + 10 + a + 11 + a + 12 + a + 13 + a + 14}}{5} \cr & = \frac{{5a + 50 + 10}}{5} \cr & {\text{From equation }}\left( {\text{i}} \right) \cr & = \frac{{5x + 50}}{5} \cr & = x + 10 \cr} $$