In a mixture of 50 liters of alcohol, the ratio of alcohol and water is 3 : 2.…
2025
In a mixture of 50 liters of alcohol, the ratio of alcohol and water is 3 : 2. What amount of water should be added to make the ratio of 2 : 3?
- A.
15 liters
- B.
20 liters
- C.
25 liters
- D.
30 liters
Attempted by 12 students.
Show answer & explanation
Correct answer: C
Solution: step-by-step
Compute the amount of alcohol in the initial 50 liters: 3/(3+2) × 50 = 3/5 × 50 = 30 liters.
Compute the initial amount of water: 50 − 30 = 20 liters.
Let x be the liters of water to add. After adding, water = 20 + x liters and alcohol remains 30 liters.
Set up the required ratio: 30/(20 + x) = 2/3. Cross-multiply and solve: 3×30 = 2×(20 + x) ⇒ 90 = 40 + 2x ⇒ 2x = 50 ⇒ x = 25.
Check: water becomes 20 + 25 = 45, so ratio = 30:45 = 2:3. Therefore, 25 liters of water should be added.