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Given below are three quantities named A, B and C. Based on the given information, determine the relation among the three quantities. Quantity A∶  A 30 litre mixture of wine and water has wine and water in the ratio 5∶ 7. How much water must be drawn off so that the ratio of wine and water becomes 25∶ 19? Quantity B∶ A 35 litre mixture of wine and water has wine and water in the ratio 1∶ 3. How much water must be drawn off so that the ratio of wine and water becomes 1.75∶ 3.35? Quantity C∶ A 27 litre mixture of wine and water has wine and water in the ratio 3∶ 2. How much water must be drawn off so that the ratio of wine and water becomes 81∶ 11?

Given below are three quantities named A, B and C. Based on the given information, determine the relation among the three quantities. Quantity A∶  A 30 litre mixture of wine and water has wine and water in the ratio 5∶ 7. How much water must be drawn off so that the ratio of wine and water becomes 25∶ 19? Quantity B∶ A 35 litre mixture of wine and water has wine and water in the ratio 1∶ 3. How much water must be drawn off so that the ratio of wine and water becomes 1.75∶ 3.35? Quantity C∶ A 27 litre mixture of wine and water has wine and water in the ratio 3∶ 2. How much water must be drawn off so that the ratio of wine and water becomes 81∶ 11? Correct Answer B > C > A

Quantity A∶ Total mixture = 30 litres. Ratio of wine∶ water = 5∶ 7

Let the total mixture be 12 units, then multiplication factor = 30/12 = 2.5

Thus, our 1 unit = 2.5 units of question.

The actual quantity of wine and water respectively = 5 × 2.5 and 7 × 2.5 = 12.5 litres and 17.5 litres respectively.

Final ratio after some water has been drawn off = 25∶ 19.

Let the actual quantities in the final mixture be 25a and 19a respectively.

As the amount of wine has not changed, this its value must be the same in the final mixture as well.

⇒ 25a = 12.5

⇒ a = 0.5

Thus, actual quantities of wine and water in the final mixture = 25 × 0.5 and 19 × 0.5 = 12.5 litres and 9.5 litres.
Thus, amount of water drawn off = (17.5 – 9.5) litres = 8 litres. A = 8 litres.

Quantity B∶ Total mixture = 35 litres. Ratio of wine∶ water = 1∶ 3

Let the total mixture be 4 units, then multiplication factor = 35/4 = 8.75

Thus, our 1 unit = 8.75 units of question.

The actual quantity of wine and water respectively = 1 × 8.75 and 3 × 8.75 = 8.75 litres and 26.25 litres respectively.

Final ratio after some water has been drawn off = 35∶ 67.

Let the actual quantities of wine and water in the final mixture be 35a and 67a respectively.

As the amount of wine has not changed, this its value must be the same in the final mix as well.

⇒ 35a = 8.75

⇒ a = 0.25

Thus, actual quantities of wine and water in the final mixture = 35 × 0.25 and 67 × 0.25 = 8.75 litres and 16.75 litres.

Thus, the amount of water drawn off = (26.25 – 16.75) litres = 9.5 litres.

B = 9.5 litres.

Quantity C∶ Total mixture = 27 litres. Ratio of wine∶ water = 3∶ 2

Let the total mixture be 5 units, then multiplication factor = 27/5 = 5.4

Thus, our 1 unit = 5.4 units of question.

The actual quantity of wine and water respectively = 3 × 5.4 and 2 × 5.4 = 16.2 litres and 10.8 litres respectively.

Final ratio after some water has been drawn off = 81∶ 11.

Let the actual quantities of wine and water in the final mixture be 81a and 11a respectively.

As the amount of wine has not changed, this its value must be the same in the final mix as well.

⇒ 81a = 16.2

⇒ a = 0.20

Thus, actual quantities of wine and water in the final mixture = 81 × 0.20 and 11 × 0.20 = 16.2 litres and 2.2 litres.

Thus, amount of water drawn off = (10.8 – 2.2) litres = 8.6 litres. C = 8.6 litres.

B > C > A. Thus, option III is correct.

 

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