Question : In a 64 L mixture, the alcohol and water are in the ratio of 1 : 3 respectively. 32 L of the mixture is taken off and replaced with 16 L of water. What is the new ratio of alcohol and water respectively?
Option 1: 1 : 5
Option 2: 5 : 12
Option 3: 2 : 7
Option 4: 3 : 10
Correct Answer: 1 : 5
Solution :
The ratio of alcohol and water = 1 : 3
Let $k$ and $3k$ be the quantity of alcohol and water.
⇒ $k+3k = 64$
⇒ $4k = 64$
⇒ $k = 16$
Quantity of alcohol and water = 16 L and 48 L
If 32 L of the mixture is taken off and replaced with 16 L of water
32 L of the mixture = 8 L alcohol and 24 L water
On adding 16 L of water to the mixture,
Quantity of alcohol = 16 – 8 = 8 L
Quantity of water = 48 – 24 + 16 = 40 L
Ratio = 8 : 40 = 1 : 5
Hence, the correct answer is 1 : 5.
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