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In a mixture of 80 litres, milk and water were in the ratio of 2 : 3. If 25% of the mixture is replaced with the same amount of milk, then what is the amount of milk in the final mixture?
1. 44 litres
2. 46 litres
3. 54 litres
4. 56 litres
5. None of these

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Correct Answer - Option 1 : 44 litres

Given:

Initial quantity of mixture = 80 litres

Ratio of milk and water in the initial mixture = 2 : 3

Amount of mixture replaced with milk = 25%

Concept used:

If a fraction of mixture is removed from the mixture, then the ratio of milk and water will be same as previous.

Calculations:

Amount of mixture replaced with milk = 25% × 80

⇒ 20 litres

After removing 20 litres,

Ratio of milk and water in the remaining mixture of 60 litres will be in the ratio of 2 : 3

Let amount of milk and water be 2x and 3x litres respectively.

⇒ 2x + 3x = 60

⇒ 5x = 60

⇒ x = 12

New amount of milk = 2x

⇒ 2 × 12

⇒ 24 litres

New amount of water = 3x

⇒ 3 × 12

⇒ 36 litres

New amount of water = 36 litres

After adding 20 litres of milk in the new mixture,

New amount of milk in the final mixture = 24 + 20

⇒ 44 litres

∴ The amount of milk in the final mixture is 44 litres.

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