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There are two solutions of acid and water, one contains acid and water in the ratio 3 ∶ 5 and the other contains acid and water in the ratio 1 ∶ 3. Equal quantities of these two solutions are mixed in a vessel. From this resulting solution, 704 ml is taken out and mixed with 88 ml of water in another vessel. What is the ratio of acid and water in the final vessel?

There are two solutions of acid and water, one contains acid and water in the ratio 3 ∶ 5 and the other contains acid and water in the ratio 1 ∶ 3. Equal quantities of these two solutions are mixed in a vessel. From this resulting solution, 704 ml is taken out and mixed with 88 ml of water in another vessel. What is the ratio of acid and water in the final vessel? Correct Answer 5 : 13

Given:

The ratio of acid to water in the first solution = 3 ∶ 5

The ratio of acid to water in the second solution = 1 ∶ 3

Equal quantities of these two solutions are mixed in a vessel. From this resulting solution, 704 ml is taken out and mixed with 88 ml of water.

Calculation:

The ratio of acid to water in the first solution = 3 ∶ 5      ---- (1)

The ratio of acid to water in the second solution = 1 ∶ 3      ---- (2) × 2

Multiply by 2 in equation (2) to make the total quantity of first and second solution the same

The ratio of acid to water in the second solution = 2 ∶ 6

The ratio of acid to water if both solution mixed in new vessel = (3 + 2) ∶ (5 + 6) = 5 ∶ 11

If 704 ml of solution is taken out in the mixed solution

Quantity of acid taken out from the mixed solution = 704 × (5/16) = 220 ml

Quantity of water taken out from the mixed solution = 704 – 220 = 484 ml

Now, 88 ml water is added to this mixture

New quantity of water = 484 + 88 = 572 ml

Ratio of acid to water = 220 ∶ 572 = 5 ∶ 13

∴ The ratio of acid and water in the final solution is 5 ∶ 13.

 

Important Points  Final 88 ml of water is mixed with the taken out quantity from the mixed solution in order to make final solution.

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