An 85 liter mixture of alcohol and water contains 20% water. How much water (in liters) must be added to this mixture so that the resulting mixture is 25% water?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e
.
Total mixture = 85 liters
Water = 20% of 85 = 17 liters
Alcohol = 85 - 17 = 68 liters
After adding x liters of water:
New total = 85 + x liters
New water = 17 + x liters
Water to be 25% of the new total = (17 + x) / (85 + x) = 0.25
⇒ 17 + x = 0.25 × (85 + x)
⇒ 17 + x = 21.25 + 0.25x
⇒ x - 0.25x = 21.25 - 17
⇒ 0.75x = 4.25
⇒ x = 4.25 ÷ 0.75
⇒ x =
liters (approx)