Let x1, x2,x3,...,xn be the n observations. Mean=X=x1+x2+...+xnn ⇒x1+x2+x3+...+xn=nX If the first item is increased by 1, second by 2 and so on. Then, the new observations are x1+1, x2+2,x3+3,...,xn+n. New mean = x1+1+ x2+2+x3+3+...+xn+nn =x1+x2+x3+...+xn+1+2+3+...+nn=nX+nn+12n=X+n+12 Hence, the correct answer is (c).