DSE 2011 Question 57: Harrod–Domar and Solow growth models

Setup, from Q55 of the paper:

Consider an economy with aggregate production $Y_{t}=A(K_{t})^{\alpha}(L_{t})^{1-\alpha}$, $A>0$, $0<\alpha<1$, both factors fully employed. A constant fraction $s$ of output is saved and invested, augmenting next period's capital; there is no depreciation. Labour grows at constant rate $n$. Let $A=20$, $\alpha=\tfrac{1}{2}$, $s=\tfrac{1}{4}$, $n=\tfrac{1}{10}$. The steady state level of output per worker is

(Same Solow economy.) The golden rule value of capital per worker is