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The balance sheet on the first day would be:

After day 2, the balance sheet would change because of further $35 million investment in mortgage.

To avoid insolvency, the regulators provided the bank with $27 million in bank capital. But the spread of news regarding mortgages leads to a bank run. People have withdrawn $40 million of deposits.

Because of this the new balance sheet would look like:

With the bank run, the checkable deposits fell to $80 million.

The capital ratio can be obtained as follow:

$\frac{18}{98}脳100=18.37\%$

Now, if the bank capital is 10% then assume bank capital to be x.

$$\begin{gathered} \frac{x}{80+x}=0.1 \\ x=8+0.1x \\ 0.9x=8 \\ x=8.89 \end{gathered}$$

So, for the capital ratio to be 10% bank capital should be $8.89 million.

Since, the capital ratio is already higher than this amount, no additional capital is required.