Are the pari of ratio in proportion ? If yes, write their middle terms and exterme terms.
2000 paise to 80 rupees and `1.2kg ` to 2400 m

Answer

To determine if the pairs of ratios are in proportion, we will follow these steps:

### Step 1: Write the ratios
We have two pairs of ratios:
1. 2000 paise to 80 rupees
2. 1.2 kg to 2400 m

### Step 2: Convert the units to the same measurement
For the first ratio, we need to convert 80 rupees into paise.
- Since 1 rupee = 100 paise, we have:
\[ 80 \text{ rupees} = 80 \times 100 = 8000 \text{ paise} \]
So, the first ratio becomes:
\[ \frac{2000 \text{ paise}}{8000 \text{ paise}} \]

For the second ratio, we need to convert 1.2 kg into grams.
- Since 1 kg = 1000 grams, we have:
\[ 1.2 \text{ kg} = 1.2 \times 1000 = 1200 \text{ grams} \]
So, the second ratio becomes:
\[ \frac{1200 \text{ grams}}{2400 \text{ meters}} \]

### Step 3: Simplify both ratios
For the first ratio:
\[ \frac{2000}{8000} = \frac{1}{4} \]

For the second ratio:
\[ \frac{1200}{2400} = \frac{1}{2} \]

### Step 4: Compare the two simplified ratios
Now we have:
1. First ratio: \(\frac{1}{4}\)
2. Second ratio: \(\frac{1}{2}\)

Since \(\frac{1}{4} \neq \frac{1}{2}\), the ratios are not in proportion.

### Step 5: Identify middle terms and extreme terms
In the proportion \(a:b = c:d\), the middle terms are \(b\) and \(c\), and the extreme terms are \(a\) and \(d\).

In our case:
- For the first ratio \(2000 \text{ paise} : 8000 \text{ paise}\), the extreme terms are \(2000\) and \(8000\).
- For the second ratio \(1200 \text{ grams} : 2400 \text{ meters}\), the extreme terms are \(1200\) and \(2400\).

### Final Answer
The pairs of ratios are not in proportion.
- Middle terms: \(8000\) and \(1200\)
- Extreme terms: \(2000\) and \(2400\)

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