An alloy of gold and silver weight 50 g. It contains 80% gold. How much gold should be added to the alloy so that percentage of gold is increased to 90 ?

Quantity of gold in the alloy :
= 80% of 50 g
= $$\left( {\frac{{80}}{{100}} \times 50} \right)$$  g
= 40 g
Let x g of gold be added
Then,
$$\eqalign{ & \Rightarrow \frac{{40 + x}}{{50 + x}} = \frac{{90}}{{100}} \cr & \Rightarrow \frac{{40 + x}}{{50 + x}} = \frac{9}{{10}} \cr & \Rightarrow 400 + 10x = 450 + 9x \cr & \Rightarrow x = 50 \cr} $$