If 3 kg of metal, which is one-third silver and the rest aluminium, is mixed with 7 kg of another metal, which is two-seventh silver and the rest is aluminium. What is the ratio of silver to aluminium in the mixture?

Given If 3 kg of metal, which is one-third silver and the rest aluminium, is mixed with 7 kg of another metal, which is two-seventh silver and the rest is aluminum.

The amount of silver is $3\left(\frac{1}{3}\right)+7\left(\frac{2}{7}\right)=1+2=3$

The amount of aluminium is $3\left(\frac{2}{3}\right)+7\left(\frac{5}{7}\right)=2+5=7$

The ratio of silver to aluminum is $\boxed{\mathbf{3}\mathbf{:}\mathbf{7}}$