Taking example here also give ansing easy
Say
$X= \left [ 2,3,4,4,5 \right ]$
and value of $a=2 , b=100$
So, according to question $Y= \left [ 104,106,108,108,110 \right ]$
Now come to option
A) correct, because for X mode is 4 and for Y mode is 108 which has same index position
B) correct , because for X median is 4and for Y median is 108 which has same index position
C) both gives mean =107.2
D) will be incorrect in option elimination
and also by calculation
$\sigma _{y}=0$
while $a\sigma _{x}+b=2.28$
https://gradestack.com/Class-11th-Commerce/Measures-of-Central/Relative-Position-of/17644-3574-27377-study-wtw
https://en.wikipedia.org/wiki/Standard_deviation