A mixture of 70 litres of wine and water contains 10% water. How much water must be added so that water becomes 37% of the final mixture?

Initially, water $=10\%$ of 70 litres $=7$ litres, so wine $=63$ litres. If $x$ litres of water are added, then water becomes $7+x$ and total mixture becomes $70+x$. So $\frac{7+x}{70+x}=\frac{37}{100}$. Solving gives $100(7+x)=37(70+x)$, so $700+100x=2590+37x$, hence $63x=1890$ and $x=30$.