Explanation

(c)
$\overline{x} = \frac{Sum\ of\ quantities}{n} = \frac{\frac{n}{2}(a + 1)}{n}$
$= \frac{1}{2}\lbrack 1 + 1 + 100d\rbrack = 1 + 50d$
$\therefore MD = \frac{1}{n}\Sigma|^{'}x_{i} - \overline{x|}$
$\Rightarrow 255 = \frac{1}{101}\lbrack 50d + 49d + \ldots + d + 0 + d + \ldots + 50d\rbrack$
$= \frac{2d}{101}\left\lbrack \frac{50 \times 51}{2} \right\rbrack$
$\Rightarrow d = \frac{255 \times 101}{50 \times 51} = 10.1$