Currently, the average time between failures of a part is $100$ hours and the average repair time is $4$ hours. A designer estimates that she can $($a$)$ increase the average time between failures by $5$ percent at a cost of $$450,$ or $($b$)$ reduce the average repair time by $10$ percent at a cost of $$200.$ Which option of the two would be more cost$-$effective?

Option a

Option b

They are the same

No enough information