A vessel contains 80 litres of a mixture of alcohol and water in the ratio of 3 : 7. If 40 litres of the mixture is taken out from the vessel and replaced with 40 litres of water, then the ratio of alcohol and water becomes:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e 3:17.
The total volume of the mixture is 80 liters. The ratio of alcohol to water is 3:7.
Alcohol: (3/10) × 80 liters = 24 liters and Water: (7/10) × 80 liters = 56 liters
40 liters of the mixture is removed. When a mixture is removed, the components are taken out in the same ratio.
Alcohol removed: (3/10) × 40 liters = 12 liters and Water removed: (7/10) × 40 liters = 28 liters
Now,
Alcohol remaining: 24 - 12 = 12 liters and Water remaining: 56 - 28 = 28 liters
40 liters of water is added back into the vessel.
Alcohol in final mixture: 12 liters (unchanged)
Water in final mixture: 28 + 40 = 68 liters
The new ratio of alcohol to water = 12:68 = 3 : 17