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Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. What is the quantity of whisky in the final mixture? I. In a vessel A whisky is 3/5th of the total mixture and 15 litres of mixture is taken out and same quantity of water is mixed into it. The content of vessel A is put into a container having whisky and water in the ratio 2 ∶ 1. II.The capacity of the container is 36 litre in which content of vessel is poured now in the resultant mixture water is 1 litre more than the whisky.   

Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. What is the quantity of whisky in the final mixture? I. In a vessel A whisky is 3/5th of the total mixture and 15 litres of mixture is taken out and same quantity of water is mixed into it. The content of vessel A is put into a container having whisky and water in the ratio 2 ∶ 1. II.The capacity of the container is 36 litre in which content of vessel is poured now in the resultant mixture water is 1 litre more than the whisky.    Correct Answer <p>If the data in both statements I and II together are needed to answer the question.</p>

Using statement I

In-vessel A

⇒ Let the total capacity of the vessel be x

3/5th part is whisky and rest is water 

∴ Whisky in the mixture = (3/5) × x = 3x/5

Water in the mixture = (2/5) × x = 2x/5

15 litre of the mixture is taken out and the quantity of contents will be removed in the same ratio

⇒ Quantity of whisky removed = (3/5) × 15 = 9 litre

⇒ Quantity of water removed = (2/5) × 15 = 6 litre

∴ Whisky in the new mixture = (3x/5) – 9

Water in the new mixture = (2x/5) – 6 

Now, 15 litre of water is added

⇒ Water in mixture = (2x/5) – 6 + 15 = (2x/5) + 9

The content of vessel A is put into a container having whisky and water in the ratio 2 ∶ 1

⇒ Let the whisky and water in the mixture be 2y and y respectively.

∴  Total whisky in final mixture = (3x/5) – 9 + 2y

Total water in the final mixture = (2x/5) + 9 + y

Statement I alone is not sufficient to answer the question

 

Using statement II

The capacity of the container is 36 litre in which content of vessel is poured now in the resultant mixture water is 1 litre more than the whisky

Statemnt II alone is not sufficient to answer the question 

 

Using statement I and statement II together

Capacity of container = 36 litre

Ratio of whisky and water = 2 ∶ 1

⇒ Quantity of whiskey = (2/3) × 36 = 24 ltr

Quantity of water = (1/3) × 36 = 12 ltr

∴ Total whisky in final mixture = (3x/5) – 9 + 24 = (3x/5) + 15

Total water in the final mixture = (2x/5) + 9 + 12 = (2x/5) + 21

 In the resultant mixture water is 1 litre more than the whisky

⇒ (2x/5) + 21 – (3x/5) – 15 = 1

⇒ x/5 = 5

⇒ x = 5

∴ Quantity of whiskey in the final mixture = (3 × 25)/5 + 15 = 30 ltr

∴ The data in both statements I and II together are needed to answer the question.

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