Hi,
Let the series be x1,x2,...,xn
mean be m and standard deviation be d
If all the elements are added or subtracted by the same quantity(say a), new mean will be m+a
the deviations of each element will still be (x1+a)-(m+a),(x2+a)-(m+a),....(xn+a)-(m+a)i.e. same as (x1-m), (x2-m)...(xn-m). So S.D. will remain same irrespective of the value of quantity added(a).
Use he same principle here.
Hence, A

let the numbers be (1,2,3) changed numbers are (6,7,8).as you can see deviation from the mean has not changed,remaining the same 1 here in both the cases.Thus d it is.

Tips :

deviation for addition,subtraction never changes if the deviation is done by a constant quantity.

deviation increases if the constant (k) is positive integer, and each number is multiplied by that number.
d*k will be the value.

deviation decrease if a constant divides each number. d/k will be the value.

since the set is inc by same constant the S.D will remain same.