Answer
Population B's sample size must be 4 times larger than population A's.
Work Step by Step
$n=(\frac{t_{\frac{α}{2}}.s}{E})^2$
We do not know the values of $t_{\frac{α}{2}}$ and $E$, but we are assuming they are the same in both cases.
$n_A=(\frac{t_{\frac{α}{2}}\times5}{E})^2=25(\frac{t_{\frac{α}{2}}}{E})^2$
$n_B=(\frac{t_{\frac{α}{2}}\times10}{E})^2=100(\frac{t_{\frac{α}{2}}}{E})^2$
$\frac{n_B}{n_A}=\frac{100(\frac{t_{\frac{α}{2}}}{E})^2}{25(\frac{t_{\frac{α}{2}}}{E})^2}=\frac{100}{25}=4$
