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In a bar, the owner instructs the waiter to always prepare the drink having 30% alcohol concentration for teenagers. Rest must be water. However a newly hired waiter prepares a 50% concentrated drink. The manager observes this and asks the waiter to decrease the concentration to prescribed level. If the drink prepared had initial volume of 1.74 litres, what will be the volume of added water after attaining the prescribed concentration? Dilution is done by using water only.

In a bar, the owner instructs the waiter to always prepare the drink having 30% alcohol concentration for teenagers. Rest must be water. However a newly hired waiter prepares a 50% concentrated drink. The manager observes this and asks the waiter to decrease the concentration to prescribed level. If the drink prepared had initial volume of 1.74 litres, what will be the volume of added water after attaining the prescribed concentration? Dilution is done by using water only. Correct Answer 1.16 litres

Initial volume of drink = 1.74 litres

Initial Concentration = 50%

Initial volume of alcohol = 1.74/2 = 0.87 litres

Initial volume of water = 0.87 litres

Final volume of alcohol = 0.87 litres

Concentration = 30%

Let the final volume of mixture be x liters.

∴ Amount of alcohol in drink = 0.3 × x = 0.3x litres

⇒ 0.87 = 0.3x

∴ x = 2.9 litres

Final volume of drink = 2.9 litres

∴ Amount of water added = 2.9 − 1.74 = 1.16 litres

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