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X and Y are two vessels containing 40% and 30% of alcohol concentration respectively. The ratio of the capacities of vessel X and Y is 2 : 3 respectively. When the solutions in vessels X and Y are mixed in another vessel Z and 18 liters of water is added it, then the final ratio of alcohol to water is 1 : 3. Find the initial quantity of alcohol in a vessel X (in liters).

X and Y are two vessels containing 40% and 30% of alcohol concentration respectively. The ratio of the capacities of vessel X and Y is 2 : 3 respectively. When the solutions in vessels X and Y are mixed in another vessel Z and 18 liters of water is added it, then the final ratio of alcohol to water is 1 : 3. Find the initial quantity of alcohol in a vessel X (in liters). Correct Answer 8

GIVEN :

The ratio of the capacities of vessel X and Y is 2 : 3 respectively.

Let the volume of solution in Vessels X and Y be 2x and 3x.

X and Y are two vessels containing 40% and 30% of alcohol concentration.

 

CONCEPT :

Mixture and Ratio

 

CALCULATION :

Ratio of alcohol to water in the two vessels is

⇒ :  = 1.7x : 3.3x

The solutions in vessels X and Y are mixed in another vessel Z and 18 liters of water is added it, 

⇒ Ratio = 1.7x : 3.3x + 18

The final ratio of alcohol to water is 1 : 3,

⇒ 1.7x : 3.3x + 18 = 1 : 3

⇒ x = 10

Initial quantity of alcohol in vessel X = 40% of 2 × 10  = 8 Liters

 

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