A 60 litre solution of alcohol and water contains 20 litres of alcohol. How much alcohol must be added to produce a solution of 50% alcohol ?

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Solution

Total solution = 60 L
Alcohol in solution = 20 L
Let x L alcohol must be added to produce 50% alcohol.
Then alcohol in solution at last = (x + 20) L
Total solution at last = (60 + x) L
Now,
Alcohol at last is equal to 50% of total solution.
x + 20 = 50(60 + x)/100
⇒ x + 20 = (60 + x)/2
⇒ x + 20 = 30 + x/2
⇒ x - x/2 = 30 - 20
⇒ (2x - x)/2 = 10
⇒ x/2 = 10
⇒ x = 10 * 2
⇒ x = 20

Therefore, 20L of alcohol must be added in 60L solution to get 50% alcohol in the solution.

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