# In a 200 litres mixture the ratio of alcohol and water is 1 ∶ 4 respectively. 40 liters of mixture is taken out and replaced with 40 litres of water.

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In a 200 litres mixture the ratio of alcohol and water is 1 ∶ 4 respectively. 40 liters of mixture is taken out and replaced with 40 litres of water. What is the new ratio of alcohol and water respectively?
1. 4 ∶ 21
2. 21 ∶ 4
3. 11 ∶ 4
4. 4 ∶ 11
5.

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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 are taken out and replaced by water.

After  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