Correct Answer - Option 2 : 150
Solution:
Given:
Initial mixture = 25% water
Joey replaces = 25% of mixture with water
Capacity of glass = 25 ml
Lemonade concentration = 30% water
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)
∴ 150 glasses of lemonade can be made