$(1)\frac{1}{6}:\frac{1}{3}=\frac{1}{5}:x$
$\frac{1}{6}x=\frac{1}{3}\times \frac{1}{5}$
$\frac{1}{6}x\div \frac{1}{6}=\frac{1}{15}\div \frac{1}{6}$
$x=\frac{2}{5}$
$(2)\frac{7.5}{1.5}=\frac{x}{3}$
$1.5x=7.5\times 3$
$1.5x\div 1.5=22.5\div 1.5$
$x=15$
$(3)x:0.24=0.05:0.03$
$0.03x=0.24\times 0.05$$0.03x\div 0.03=0.012\div 0.03$
$x=0.4$