Correct Answer - Option 1 : 4 ∶ 21
Given:
Quantity of pure milk = 144 litres
16 litres of milk is replaced by water 3 times.
Formula used:
Suppose a container contains A units of a liquid from which B units are taken out and replaced by water.
After n operations, operations, operations,
Quantity of pure liquid in the final mixture = A {1 – (B/A)}n
Calculation:
Let the alcohol and water be x and 4x
⇒ x + 4x = 200 liters
⇒ 5x = 200
⇒ x = 40 liters
⇒ The amount of alcohol = x = 1 × 40 = 40 liters
⇒ The amount of water = 4x = 4 × 40 = 160 liters
According to the question,
40 liters of mixture is taken out and replaced with 40 liters of water
⇒ The total quantity of mixture = 200 liters
Quantity of alcohol taken out = 40 × (40/200) = 8 liters
⇒ Quantity of water is taken out = 160 × (40/200) = 32 liters
Remaining quantity of alcohol = 40 liters - 8 liters = 32 liters
Now, 40 litres of mixture is taken out and replaced with 40 litres of water
Quantity of water = 160 liters - 32 liters + 40 liters = 168 liters
New ratio of alcohol and water = 32 ∶ 168 = 4 ∶ 21
∴ The new ratio of alcohol and water is 4 ∶ 21