How many liters of 60% alcohol solution should be added to 40 liters of a 20% alcohol solution to make a 50% solution?

Exactly 80 liters of 20% are needed.

Let quantity of 20% alcohol solution be added : x liters  

Here is the work:

> x*20% + 40 * 50% = (x+40) * 30%  

> x*0.2 + 40*0.5 = (x+40)*0.3 ..(converting percentages into decimal)  

> 0.2x + 20 = 0.3x + 12

> 20-12 = 0.3x - 0.2x (Rearranging similar terms)

> 8 = 0.1 x

Hence x = 8/0.1  

Ans 80 Litres