Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
200 mL : 2.5 litre and Rs. 4: Rs. 50

Answer

To determine if the ratios \(200 \, \text{mL} : 2.5 \, \text{litre}\) and \(Rs. 4 : Rs. 50\) form a proportion, we will follow these steps:

### Step 1: Convert the units to the same measurement
We need to convert \(2.5 \, \text{litre}\) to milliliters since the first term is in milliliters.

1 liter = 1000 milliliters

Therefore,
\[ 2.5 \, \text{litre} = 2.5 \times 1000 = 2500 \, \text{mL} \]

### Step 2: Write the ratios in fraction form
Now we can express the ratios as fractions:

1. The first ratio is:
\[ \frac{200 \, \text{mL}}{2500 \, \text{mL}} = \frac{200}{2500} \]

2. The second ratio is:
\[ \frac{Rs. 4}{Rs. 50} = \frac{4}{50} \]

### Step 3: Simplify the fractions
Now we simplify both fractions:

1. For \(\frac{200}{2500}\):
- Divide both the numerator and denominator by 100:
\[ \frac{200 \div 100}{2500 \div 100} = \frac{2}{25} \]

2. For \(\frac{4}{50}\):
- Divide both the numerator and denominator by 2:
\[ \frac{4 \div 2}{50 \div 2} = \frac{2}{25} \]

### Step 4: Check if the fractions are equal
Since both simplified fractions are equal:
\[ \frac{2}{25} = \frac{2}{25} \]
This means that the ratios \(200 \, \text{mL} : 2.5 \, \text{litre}\) and \(Rs. 4 : Rs. 50\) are in proportion.

### Step 5: Identify the middle and extreme terms
In the proportion \(200 \, \text{mL} : 2500 \, \text{mL} :: Rs. 4 : Rs. 50\):
- The **extreme terms** are the first and last terms: \(200 \, \text{mL}\) and \(Rs. 50\).
- The **middle terms** are the second and third terms: \(2500 \, \text{mL}\) and \(Rs. 4\).

### Final Answer
- The ratios form a proportion.
- **Extreme terms**: \(200 \, \text{mL}\) and \(Rs. 50\)
- **Middle terms**: \(2500 \, \text{mL}\) and \(Rs. 4\)

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