How much interest rate would make his earnings the same A rural landowner can deposit his savings in a commercial bank and receive an annual interest rate of 8%. Alternatively he can lend to
villagers who need credit. If all loans are of the same size and only sixty per
cent of them are repaid, the how much interest rate would make his earnings the same as from depositing his savings in a bank?

I took the case that suppose landowner has 100 dollars and he is landing to one villager for one year, then if he deposits in bank for a year he gets 108 after one year, but if he gives it to villager, he gets 60 dollars back as given and to compensate he must have charged 48%, so that total is 108 dollars. But answer given for this question is 80%? Why is that?
I don't know how you got 48% (and it would have been appropriate to include your work in your question), but think about it intuitively. Take your second to last step. If the landowner lends to the villagers and on average gets 60 dollars plus interest back, then if the interest rate was 80%, you'd get 60 + 48 = 108 dollars, the same as depositing to the commercial bank.

Algebraically, here's how you'd set up solving for $r$:

$$(100 \cdot (1+r))0.6 + 0(0.4) = 108$$

Where you have a 60% chance of being paid back 100 with interest. Then you just solve.