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 ?

Answer: Option C

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,
$$\begin{array}{rl}& \Rightarrow \frac{40+x}{50+x}=\frac{90}{100}\\ & \Rightarrow \frac{40+x}{50+x}=\frac{9}{10}\\ & \Rightarrow 400+10x=450+9x\\ & \Rightarrow x=50\end{array}$$