Question

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?​

Answer 1

x = 20

Step-by-step explanation:

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.

Answer 2

Answer:

x = 20

Step-by-step explanation:

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