Just think of the payoffs to each of the claimant parties under the boom and bust scenarios.
Boom, the corp ends up with 60 cash units; pays its debt in full (40) and liquidates with the shareholders getting 20.
Bust, the ending cash is 30 which of course goes to the debt in its entirety. Shareholders get zippo.
So the debtholder gets either 40 or 30; shareholder gets either 20 or 0; and each with a probability of 1/2. From that, the expected values of each as given in the answer (35 and 10, resp.) immediately follow.
As to your first question/doubt, I suppose it's to point out that the total value of the firm's assets (1/2 x 30 + 1/2 x 60) is always equal to the total value of all the claimholders' interests (35 + 10). That's an important identity to keep in mind.
By the way, these asymmetric payoff 'profiles' to the debt and equity that you see here will be important later if you study option theory. Best of luck!
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