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To solve this question, we need to find the density of the combined liquid \( C \), which results from mixing liquids \( A \) and \( B \).

### Step 1: Determine the volume of liquid A
We are given:
- Density of liquid \( A \) (\( \rho_A \)) = 70 kg/m³
- Mass of liquid \( A \) (\( m_A \)) = 1400 kg

Using the formula:
\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}} \quad \Rightarrow \quad V_A = \frac{m_A}{\rho_A}
\]

Substitute the values:
\[
V_A = \frac{1400}{70} = 20 \, \text{m}^3
\]

### Step 2: Determine the mass of liquid B
We are given:
- Density of liquid \( B \) (\( \rho_B \)) = 280 kg/m³
- Volume of liquid \( B \) (\( V_B \)) = 30 m³

Using the density formula again, the mass of liquid \( B \) is:
\[
m_B = \rho_B \times V_B = 280 \times 30 = 8400 \, \text{kg}
\]

### Step 3: Find the total mass and total volume
- Total mass of liquid \( C \) = \( m_A + m_B = 1400 + 8400 = 9800 \, \text{kg} \)
- Total volume of liquid \( C \) = \( V_A + V_B = 20 + 30 = 50 \, \text{m}^3 \)

### Step 4: Calculate the density of liquid C
The density of liquid \( C \) is given by:
\[
\text{Density of C} = \frac{\text{Total mass of C}}{\text{Total volume of C}} = \frac{9800}{50} = 196 \, \text{kg/m}^3
\]

### Final Answer:
The density of liquid \( C \) is **196 kg/m³**.

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Would you like more details or have any other questions?

Here are 5 related questions:
1. How does changing the volume of liquid B affect the density of liquid C?
2. What if liquid A had a different mass but the same density?
3. How would you solve this problem if both liquids had the same density?
4. Can the density of liquid C ever be lower than the densities of both A and B?
5. How would adding a third liquid affect the overall density?

**Tip:** When combining liquids, the total mass and total volume both play a crucial role in determining the resulting density. Always calculate them separately before combining.

Liquid A and liquid B are mixed to make liquid C. Liquid A has a density of 70 kg/m³ and a mass of 1400 kg. Liquid B has a density of 280 kg/m³ and a volume of 30 m³. Work out the density of liquid C.

This problem involves calculating the density of liquid C by mixing liquid A and liquid B, given the densities and masses of the liquids. The problem uses key concepts such as density, mass, and volume relationships, and is suitable for students preparing for GCSE.

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