The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6...

Mean $\overset{¯}{x} = \dfrac{a + 6 + 8 + 5 + 10}{5} = 6$ (given)

$⇒ a + b = 7 . . . \left(i\right)$

Variance $= \dfrac{∑ {x}_{i}^{2}}{n} - {\left(\overset{¯}{x}\right)}^{2} = \dfrac{{a}^{2} + {b}^{2} + {8}^{2} + {5}^{2} + {10}^{2}}{5} - {6}^{2} = 6 . 8$ (given)

$⇒ {a}^{2} + {b}^{2} = 25 . . . \left(ii\right)$

on solving equations \left(i\right)& \left(ii\right), we get $a = 3, b = 4$

Now, Mean deviation about Mean $M = \dfrac{∑ \left|{x}_{i} - \overset{¯}{x}\right|}{n}$

$⇒ \dfrac{\left|3 - 6\right| + \left|4 - 6\right| + \left|8 - 6\right| + \left|5 - 6\right| + \left|10 - 6\right|}{5}$

$⇒ \dfrac{3 + 2 + 2 + 1 + 4}{5} = \dfrac{12}{5}$

$∴ M = \dfrac{12}{5} ⇒ 25M = 60$.