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Two vessels A and B contain spirit and water in the ratio 5 : 2 and 4 : 3 respectively. These contents are mixed in the ratio 7 : 5. In 420 mL of this solution, how much water should be added to get a solution of spirit and water in the ratio 11:7?

Two vessels A and B contain spirit and water in the ratio 5 : 2 and 4 : 3 respectively. These contents are mixed in the ratio 7 : 5. In 420 mL of this solution, how much water should be added to get a solution of spirit and water in the ratio 11:7? Correct Answer 30 mL

Given:

In vessel A, ratio of spirit and water = 5 : 2

In vessel B, ratio of spirit and water = 4 : 3

Ratio of spirit and water in final mixture = 7 : 5

Total content in final mixture = 420 mL

Solution:

Let content of A = 7x and content of B = 5x

⇒ 7x + 5x = 420 mL

⇒ 12x = 420

⇒ x = 35

⇒ A = 7 × 35 = 245

⇒ B = 5 × 35 = 175

Ratio of spirit : water in A = 5 : 2

⇒ Spirit in A = (5/7) × 245 = 175

⇒ Water in A = (2/7) × 245 = 70

Ratio of spirit and water in B = 4 : 3

⇒ Spirit in B = (4/7) × 175 = 100

⇒ Water in B = (3/7) × 175 = 75

⇒ Total spirit in the mixture = Spirit in A + Spirit in B

⇒ Total spirit in the mixture = 175 + 100 = 275

⇒ Total water in the mixture = Water in A + Water in B

⇒ Total water in the mixture = 70 + 75 = 145

⇒ Spirit : Water = 275 : 145

Let y mL water is added then the ratio of spirit and water will become 11 : 7

⇒ 275/(145 + y) = 11/7

⇒ 175 = 145 + y

⇒ y = 175 - 145

⇒ y = 30 mL

∴ 30 mL of water should be added to the mixture.

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