A mixture of two liquids A and B is in the ratio 4:3. If 21 liters of liquid A i

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Question: A mixture of two liquids A and B is in the ratio 4:3. If 21 liters of liquid A is added to the mixture, the ratio becomes 5:3. What was the initial volume of the mixture?

Options:

42 liters
45 liters
48 liters
50 liters

Correct Answer: 45 liters

Solution:

Let the initial volumes of A and B be 4x and 3x. After adding 21 liters to A, we have (4x + 21)/(3x) = 5/3. Solving gives x = 15, so the initial volume = 4x + 3x = 45 liters.

A mixture of two liquids A and B is in the ratio 4:3. If 21 liters of liquid A i

Practice Questions

A mixture of two liquids A and B is in the ratio 4:3. If 21 liters of liquid A is added to the mixture, the ratio becomes 5:3. What was the initial volume of the mixture?

42 liters
45 liters
48 liters
50 liters

Questions & Step-by-Step Solutions

A mixture of two liquids A and B is in the ratio 4:3. If 21 liters of liquid A is added to the mixture, the ratio becomes 5:3. What was the initial volume of the mixture?

Step 1: Understand the initial ratio of liquids A and B, which is 4:3. This means for every 4 parts of A, there are 3 parts of B.
Step 2: Let the initial volume of liquid A be 4x liters and the initial volume of liquid B be 3x liters.
Step 3: Calculate the total initial volume of the mixture, which is 4x + 3x = 7x liters.
Step 4: According to the problem, when 21 liters of liquid A is added, the new volume of A becomes (4x + 21) liters.
Step 5: The new ratio of A to B is given as 5:3. This can be written as (4x + 21)/(3x) = 5/3.
Step 6: Cross-multiply to solve the equation: 3 * (4x + 21) = 5 * (3x).
Step 7: Expand both sides: 12x + 63 = 15x.
Step 8: Rearrange the equation to isolate x: 15x - 12x = 63, which simplifies to 3x = 63.
Step 9: Solve for x: x = 63 / 3 = 21.
Step 10: Now, substitute x back to find the initial volumes: A = 4x = 4 * 21 = 84 liters and B = 3x = 3 * 21 = 63 liters.
Step 11: Calculate the total initial volume of the mixture: 84 + 63 = 147 liters.

Ratios – Understanding and manipulating ratios to find unknown quantities.
Algebraic Equations – Setting up and solving equations based on given conditions.
Volume Calculation – Calculating total volume based on individual components.

A mixture of two liquids A and B is in the ratio 4:3. If 21 liters of liquid A i

What’s inside this PDF?

A mixture of two liquids A and B is in the ratio 4:3. If 21 liters of liquid A i

Practice Questions

Questions & Step-by-Step Solutions

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