Methoxyethane on reaction with hot concentrated $HI$ gives

When ethyl bromide is treated with dry $Ag_2O$,the main product is:

According to the Lewis concept of acids and bases,ether is:

In the reaction $Ar-OH + RX \xrightarrow{\text{alkali}} A$,$A$ is

An ether $(A)$,$C_5H_{12}O$,when heated with excess of hot concentrated $HI$ produced two alkyl halides which when treated with $NaOH$ yielded compounds $(B)$ and $(C)$. Oxidation of $(B)$ and $(C)$ gave a propanone and an ethanoic acid respectively. The $IUPAC$ name of the ether $(A)$ is

In which case is methyl $t$-butyl ether formed?