A college has raised $75\%$ of the amount it needs for a new building by receiving an average donation of \ 600$fromthepeoplealreadysolicited.Thepeoplealreadysolicitedrepresent$ 60\%$ of the people the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what would be the average donation from the remaining people to be solicited?

Let the total amount needed for the building be $T$ and the total number of people to be asked be $P$.
From the given information:

* People already solicited = $60\%$ of $P=0.60P$
* Amount already raised = $75\%$ of $T=0.75T$
* Average donation of those solicited = \ 600$Therefore,thetotalamountraisedsofaris:$$0.75T=0.60P\times 600$ $

$$0.75T=360P$$

$$T=\frac{360P}{0.75}=480P$$

Now, let's find the remaining requirements:

* Remaining amount to be raised = $100\%-75\%=25\%$ of $T=0.25\times 480P=120P$
* Remaining people to be solicited = $100\%-60\%=40\%$ of $P=0.40P$

Let the required average donation from the remaining people be $A$.

$$A=\frac{\text{Remaining Amount}}{\text{Remaining People}}=\frac{120P}{0.40P}=\frac{120}{0.40}=\$300$$