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In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for both quantities and choose the correct option. Quantity A: How much water must be added to 15 litres of milk-water mixture of ratio 4 ∶ 1, such that the ratio of milk and water in mixture becomes 3 ∶ 2? Quantity B: In what quantity of alcohol-water mixture of ratio 2 ∶ 1, should 2 litres of water be added, such that the ratio of alcohol-water in the final mixture is 1 ∶ 1?

In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for both quantities and choose the correct option. Quantity A: How much water must be added to 15 litres of milk-water mixture of ratio 4 ∶ 1, such that the ratio of milk and water in mixture becomes 3 ∶ 2? Quantity B: In what quantity of alcohol-water mixture of ratio 2 ∶ 1, should 2 litres of water be added, such that the ratio of alcohol-water in the final mixture is 1 ∶ 1? Correct Answer Quantity A < Quantity B

Solving for Quantity A:

Quantity of milk in initial mixture = quantity of milk in final mixture = (4/5) × 15 = 12 litres

Quantity of water in initial mixture = (1/5) × 15 = 3 litres

Let ‘x’ litres of water be added

Quantity of water in final mixture = (x + 3) litres

Hence, milk-water ratio of final mixture = 12/(x + 3) = 3/2

⇒ 24/3 = x + 3

⇒ x = 8 - 3 = 5 litres

⇒ Quantity A = 5 litres

Solving for Quantity B:

Let the required quantity of initial mixture be ‘x’ litres

Final mixture = (x + 2) litres

Quantity of alcohol in initial mixture = quantity of alcohol in final mixture

⇒ (2/3) × x = (1/2) × (x + 2)

⇒ 4x = 3x + 6

⇒ x = 6 litres

⇒ Quantity B = 6 litres

∴ Quantity A < Quantity B

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