Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
(a) 25 cm : 1 m and Rs. 40: Rs.160

Answer

To determine if the given ratios form a proportion, we will follow these steps:

### Step 1: Understand the Ratios
The two ratios given are:
1. 25 cm : 1 m
2. Rs. 40 : Rs. 160

### Step 2: Convert Units
Since the first ratio has different units (centimeters and meters), we need to convert 1 meter into centimeters.
- 1 meter = 100 centimeters

So, we can rewrite the first ratio as:
- 25 cm : 100 cm

### Step 3: Write the Ratios as Fractions
Now, we can express both ratios as fractions:
- First ratio: \( \frac{25}{100} \)
- Second ratio: \( \frac{40}{160} \)

### Step 4: Simplify the Fractions
Now, simplify both fractions:
- \( \frac{25}{100} = \frac{1}{4} \) (by dividing both the numerator and denominator by 25)
- \( \frac{40}{160} = \frac{1}{4} \) (by dividing both the numerator and denominator by 40)

### Step 5: Compare the Fractions
Now we compare the two simplified fractions:
- \( \frac{1}{4} \) and \( \frac{1}{4} \)

Since both fractions are equal, we can conclude that the ratios form a proportion.

### Step 6: Identify the Middle and Extreme Terms
In a proportion of the form \( a : b :: c : d \):
- The extreme terms are the first and last terms (25 cm and Rs. 160).
- The middle terms are the second and third terms (100 cm and Rs. 40).

### Final Answer
The ratios form a proportion:
- \( 25 \text{ cm} : 100 \text{ cm} :: Rs. 40 : Rs. 160 \)

**Extreme Terms:** 25 cm and Rs. 160
**Middle Terms:** 100 cm and Rs. 40

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