In a division problem, the divisor is $12$ times the quotient and $9timestheremainder.Iftheremainderis$ 96$, find the dividend.

Given:
$$\text{Remainder }(R)=96$$
$$\text{Divisor }(D)=9\times R=9\times 96=864$$
Also, given that the divisor is $12$ times the quotient ($Q$):
$$D=12\times Q$$
$$864=12\times Q$$
$$Q=\frac{864}{12}=72$$
The division formula is:
$$\text{Dividend}=(\text{Divisor}\times \text{Quotient})+\text{Remainder}$$
$$\text{Dividend}=(864\times 72)+96$$
Let's calculate $864\times 72$:
$$864\times 72=62208$$
Now add the remainder:
$$\text{Dividend}=62208+96=62304$$
Hence, the dividend is $62304$.