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Two vessels A and B contains spirit and water in the ratio 5 : 2 and 8 : 5. Their contents are mixed in the ratio 7 : 2. In 520 ml of this solution, how much water should be added to make it a solution of spirit and water as 3 : 2?

Two vessels A and B contains spirit and water in the ratio 5 : 2 and 8 : 5. Their contents are mixed in the ratio 7 : 2. In 520 ml of this solution, how much water should be added to make it a solution of spirit and water as 3 : 2? Correct Answer 80 ml

Given:

Ratio of Spirit and Water in vessel A = 5 : 2

Ratio of Spirit and Water in vessel B = 8 : 5

Concept Used-

If A and B are mixed in ratio of x : y, then part of A in Mixture = x/(x + y) 

Calculation-

Part of Spirit and Water in vessel A = 5/7 and 2/7

Part of Spirit and Water in vessel B = 8/13 and 5/13

If Vessel A and Vessel B are mixed in ratio of 7 : 2 then,

Part of Spirit and Water in vessel A = 7 × 5/7 and 7 × 2/7

⇒ 5 and 2

Part of Spirit and Water in vessel B = 2 × 8/13 and 2 × 5/13

⇒ 16/13 and 10/13

Total Spirit = 5 + 16/13 = 81/13

Total Water = 2 + 10/13 = 36/13

Ratio of spirit and water in the new mixture = 81/13 : 36/13 = 9 : 4

Now, 

13 units = 520

1 units = 520/13 = 40 

9 units = 40 × 9 = 360

And 4 units = 40 × 4 = 160

Let x ml water should be added.

According to the question:

360/(160 + x) = 3/2

⇒ 160 + x = 240

⇒ x = 80 ml

∴ 80 ml water should be added so that the mixture contains spirit and water in the ratio 3 : 2.

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