If the mean deviation of the numbers $1,1+d,1+2d,\cdots +1+100d$  from their mean is 225, then the d is equal to 

Mean $=\overline{x}=\frac{1+(1+d)+\cdots +(1+100d)}{101}=\frac{101+\frac{100\times 101}{2}\times d}{101}=1+50d$

M.D from the mean $=\frac{\Sigma |x_i-\overline{x}|}{101}=\frac{50d+49d+\cdots +0+d+50d}{101}=\frac{5d\left(\frac{50\times 51}{2}\right)}{101}=\frac{50\times 51\times d}{101}$

$\therefore 255=\frac{50\times 51}{101}d\Rightarrow \frac{255\times 101}{10\times 255}=f$

$\Rightarrow d=10.1$