A pot which is full of water, weight is 28 Kg. When the pot 1 / 4 full, weight is 19 Kg. If the pot is 2 / 3 full of water then the weight is

Options

A. 8 Kg.
B. 20 Kg
C. 24 Kg
D. 18.6 Kg.

Answer

To solve the problem step by step, we need to determine the weight of the pot when it is 2/3 full of water.

### Step 1: Define Variables
Let:
- \( x \) = weight of the empty pot
- \( w \) = weight of the water when the pot is full

### Step 2: Set Up the Equations
From the information given:
1. When the pot is full of water, the total weight is 28 kg:
\[ x + w = 28 \quad \text{(1)} \]
2. When the pot is 1/4 full of water, the total weight is 19 kg:
\[ x + \frac{1}{4}w = 19 \quad \text{(2)} \]

### Step 3: Solve the Equations
We can solve these two equations to find the values of \( x \) and \( w \).

**From Equation (1):**
\[ w = 28 - x \quad \text{(3)} \]

**Substituting Equation (3) into Equation (2):**
\[ x + \frac{1}{4}(28 - x) = 19 \]
Distributing \( \frac{1}{4} \):
\[ x + 7 - \frac{1}{4}x = 19 \]
Combining like terms:
\[ \frac{3}{4}x + 7 = 19 \]
Subtracting 7 from both sides:
\[ \frac{3}{4}x = 12 \]
Multiplying both sides by \( \frac{4}{3} \):
\[ x = 16 \quad \text{(weight of the empty pot)} \]

**Now, substitute \( x \) back into Equation (3) to find \( w \):**
\[ w = 28 - 16 = 12 \quad \text{(weight of the water when full)} \]

### Step 4: Calculate Weight When Pot is 2/3 Full
Now we need to find the weight of the pot when it is 2/3 full:
\[ \text{Weight when 2/3 full} = x + \frac{2}{3}w \]
Substituting the values of \( x \) and \( w \):
\[ = 16 + \frac{2}{3} \times 12 \]
Calculating \( \frac{2}{3} \times 12 \):
\[ = 16 + 8 = 24 \]

### Final Answer
The weight of the pot when it is 2/3 full of water is **24 kg**.

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