A river barge, whose base is approximately rectangular, carries a load of grain. The barge's base is $10$ m wide by $30$ m$.$ When unloaded, its depth of submergence is $1$ m and with the load of grain it becomes $2\mathrm{.}5$ m$.$ Determine $($a$)$ the unloaded weight of the barge and $($b$)$ the weight of the grain.