Find the third proportional to :
1 kg 250 g, 500 g

Answer

To find the third proportional to 1 kg 250 g and 500 g, we can follow these steps:

### Step 1: Convert all weights to the same unit
1 kg 250 g can be converted to grams:
- 1 kg = 1000 g
- Therefore, 1 kg 250 g = 1000 g + 250 g = 1250 g

Now we have:
- First term = 1250 g
- Second term = 500 g

### Step 2: Set up the ratio
We need to find the ratio of the second term to the first term:
\[ \text{Ratio} = \frac{\text{Second term}}{\text{First term}} = \frac{500 \text{ g}}{1250 \text{ g}} \]

### Step 3: Simplify the ratio
To simplify the ratio:
\[ \frac{500}{1250} = \frac{500 \div 250}{1250 \div 250} = \frac{2}{5} \]

### Step 4: Use the ratio to find the third proportional
Let the third proportional be \( x \). According to the definition of third proportional:
\[ \frac{500}{1250} = \frac{x}{500} \]
This can be rewritten as:
\[ \frac{2}{5} = \frac{x}{500} \]

### Step 5: Cross-multiply to solve for \( x \)
Cross-multiplying gives:
\[ 2 \times 500 = 5 \times x \]
\[ 1000 = 5x \]

### Step 6: Solve for \( x \)
Now, divide both sides by 5:
\[ x = \frac{1000}{5} = 200 \]

### Final Answer
The third proportional to 1 kg 250 g and 500 g is **200 g**.

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