# In a 2 litres mixture of lemonade, water concentration is 25%. Joey removes 25% of total mixture and replaces it with water. With this mixture she wan

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In a 2 litres mixture of lemonade, water concentration is 25%. Joey removes 25% of total mixture and replaces it with water. With this mixture she wants to make lemonade having 70% water, how many glasses can be filled with this mixture if capacity of glass is 25 ml?

1. 175
2. 150
3. 250
4. 300
5. 275

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Correct Answer - Option 2 : 150

Solution:

Given:

Initial mixture = 25% water

Joey replaces = 25% of mixture with water

Capacity of glass = 25 ml

Calculation:

In 2 litres lemonade concentration of water = 0.25 × 2

⇒ Concentration of water = 0.50 litres, concentration of lemon juice = 1.5 litres (∵ 2 – 0.5 = 1.5)

⇒ 25% of mixture replaced with water; water added = 0.25 × 2.0

⇒ water added = 0.50 litres; lemon juice present = 0.75 × 0.50

⇒ Quantity of water removed = 0.5 × 0.25

⇒ Quantity of water removed = 0.125

⇒ Lemon juice removed = 0.375 litres

⇒ lemon juice in new mixture = 1.5 – 0.375

⇒ lemon juice in new mixture = 1.125 litres

⇒ Water present in new mixture = 0.5 + 0.5 - 0.125

⇒ water present in new mixture = 0.875 litres

Quantity of lemon juice in lemonade is going to remain the same hence, equating on basis of that

⇒ Assume quantity of water needs to be added as X

⇒ 0.30 × (2 + X) = 1.125

⇒ 0.6 + 0.30X = 1.125

⇒ 0.30X = 0.525

⇒ X = 0.525/ 0.30

⇒ X = 1.75 litres

Total quantity of lemonade = 2 + 1.75

⇒ Total quantity of lemonade = 3750 ml

⇒ Number of glasses = 150 (∵ 3750/ 25 = 150)