If the variance of the first n natural numbers is 10 and the...

$var\left(1, 2, \ldots n\right) = 10 ⇒ \dfrac{{1}^{2} + {2}^{2} + \ldots + {n}^{2}}{n} - {\left(\dfrac{1 + 2 + \ldots + n}{n}\right)}^{2} = 10$

$⇒ \dfrac{\left(n + 1\right)\left(2n + 1\right)}{6} - {\left(\dfrac{n + 1}{2}\right)}^{2} = 10$

$⇒ {n}^{2} - 1 = 120 ⇒ n = 11$

$var\left(2, 4, 6 \ldots . , 2m\right) = 16 ⇒ var\left(1, 2 \ldots . , m\right) = 4$

$⇒ {m}^{2} - 1 = 48 ⇒ m = 7 ⇒ m + n = 18$