Solutions A and B contain acid and water in the ratio 4 ∶ 3 and 9 ∶ 5, respectively. Four litres of solution A is mixed with 5 litres of solution B. What is the ratio of acid and water in the resulting mixture?a)4 ∶ 7b)7 ∶ 4c)11 ∶ 7d)9 ∶ 11Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Given:

Solutions A and B contain acid and water in the ratio 4 ∶ 3 and 9 ∶ 5

Calculation:

Total acid after mixing of two solution = 4 × (4/7) + 5 × (9/14)

⇒ 16/7 + 45/14

⇒ (32 + 45)/14

⇒ 77/14

⇒ 11/2

Total water after mixing of two solution = 4 × (3/7) + 5 × (5/14)

⇒ 12/7 + 25/14

⇒ (24 + 25)/14

⇒ 49/14

⇒ 7/2

Ratio = 11/2 : 7/2

⇒ 11 : 7

∴ The ratio of acid and water in the resulting mixture is 11 : 7.

Answer

To find the ratio of acid and water in the resulting mixture, we need to calculate the amount of acid and water in the individual solutions A and B, and then combine them in the given ratio.

Given:
Solution A has acid and water in the ratio 4:3.
Solution B has acid and water in the ratio 9:5.
Four litres of solution A is mixed with 5 litres of solution B.

Let's calculate the amount of acid and water in solution A and B first.

Amount of acid in solution A:
Let the amount of acid in solution A be 4x (where x is a constant).
Therefore, the amount of water in solution A will be 3x.

Amount of acid in solution B:
Let the amount of acid in solution B be 9y (where y is a constant).
Therefore, the amount of water in solution B will be 5y.

Now, let's calculate the total amount of acid and water in the resulting mixture.

Total amount of acid in the resulting mixture = 4x + 9y
Total amount of water in the resulting mixture = 3x + 5y

Given that 4 litres of solution A is mixed with 5 litres of solution B, we can set up the following equation:

4x + 9y = 4 (acid in solution A) + 5 (acid in solution B)
3x + 5y = 3 (water in solution A) + 5 (water in solution B)

Simplifying the equations, we get:

4x + 9y = 4 + 5
3x + 5y = 3 + 5

4x + 9y = 9
3x + 5y = 8

Solving these equations, we find:
x = 1/3
y = 1/2

Now, let's calculate the ratio of acid and water in the resulting mixture:

Ratio of acid = (4x + 9y) : (3x + 5y)
Ratio of acid = (4 * 1/3 + 9 * 1/2) : (3 * 1/3 + 5 * 1/2)
Ratio of acid = (4/3 + 9/2) : (1 + 5/2)
Ratio of acid = (8/6 + 27/6) : (6/6 + 15/6)
Ratio of acid = 35/6 : 21/6
Ratio of acid = 35 : 21

Ratio of water = (3x + 5y) : (3x + 5y)
Ratio of water = (3 * 1/3 + 5 * 1/2) : (3 * 1/3 + 5 * 1/2)
Ratio of water = (1 + 5/2) : (1 + 5/2)
Ratio of water = (6/2 + 15/2) : (6/2 + 15/2)
Ratio of water = 21/2 : 21/2
Ratio of water = 21 : 21

Therefore, the ratio of acid and water in the resulting mixture is 35 : 21, which simplifies to 11 : 7.

Similar SSC CGL Doubts

The ratios of alcohol to water in solutions A and B are 3 ∶ 5 and 9 ∶ 7, respectively. A and B are mixed in the ratio 5 ∶ 8. In 520 ml of the resulting solution, how much water (in ml) should be mixed so as to obtain a solution in which the ratio of alcohol to water is 3 ∶ 4?

A mixture contains wine and water in the ratio of 5 : 2 respectively and another mixture contains them in the ratio of 4 : 5 respectively. How many liters of the latter must be mixed with 35 liters of the former so that the resultant mixture must contain equal quantities of wine and water?

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A container contains a mixture of two liquids A and B in the ratio of 7 : 5. When 9 L of mixture is drawn off and the container is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the container initially ?

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