If the average of 5 consecutive integers is x.

Let number be a, a + 1, a + 2, a + 3, a + 4 Next, a + 5, a + 6, a + 7, a + 8, a + 9 Next to next – a + 10, a + 11, a + 12, a + 13, a + 14 1st condition $\begin{array}{l}=\Large\frac{5a+10}{5}=x\\ \text{5a + 10 = 5x…..(i)}\\ \text{2nd condition}\\ =\Large\frac{a+10+a+11+a+12+a+13+a+14}{5}\\ =\Large\frac{5 a+50+10}{5}\\ \text { From equation (i), }\\ =\Large\frac{5 x+50}{5}\\ =x+10 \end{array}$