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Given below are two quantities named A and B. Based on the given information, you have to determine the relationship between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: A can contains a mixture of two liquids A and B in the ratio 3 : 5. When 12 liters of mixture is drawn out and the can is filled with liquid B, the ratio of A and B becomes 1 : 3. How many liters of liquid A were contained by the can initially?  Quantity B: 9 liters

Given below are two quantities named A and B. Based on the given information, you have to determine the relationship between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: A can contains a mixture of two liquids A and B in the ratio 3 : 5. When 12 liters of mixture is drawn out and the can is filled with liquid B, the ratio of A and B becomes 1 : 3. How many liters of liquid A were contained by the can initially?  Quantity B: 9 liters Correct Answer Quantity A > Quantity B

Given:

Initial ratio (A : B) = 3 : 5

Amount of liquid drawn = 12l

Final ratio (A : B) = 1 : 3

Calculation:

Let the initial quantity of A and B be 3x and 5x.

Quantity of A left = 3x – (3/8) × 12 = (3x – 9/2) l

Quantity of B left = 5x – (5/8) × 12 = (5x – 15/2) l

A.T.Q

(3x – 9/2)/(5x – 15/2) + 12 = 1/3

⇒ (3x – 9/2)/(5x + 9/2) = 1/3

⇒ 9x – 27/2 = 5x + 9/2

⇒ 4x = 36/2

⇒ 4x = 18

⇒ x = 4.5

A's initial quantity = 3x = (3 × 4.5) liters

⇒ 13.5 litres

∴Quantity A > Quantity B 

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