In which of the following, lengths have been arranged in decreasing order ?

Question

Accepted Answer

To determine the correct arrangement of lengths in decreasing order, we need to convert all measurements to the same unit and then compare them. Let's convert all measurements to millimeters (mm) for consistency.

**Option 4: 8 m, 80 dm 8 cm, 8500 mm, 800 cm 8 mm**

1. **8 m**: 
   - 1 meter = 1000 mm
   - 8 m = 8 × 1000 mm = 8000 mm

2. **80 dm 8 cm**:
   - 1 decimeter (dm) = 100 mm
   - 80 dm = 80 × 100 mm = 8000 mm
   - 8 cm = 8 × 10 mm = 80 mm
   - Total = 8000 mm + 80 mm = 8080 mm

3. **8500 mm**: Already in millimeters.

4. **800 cm 8 mm**:
   - 1 centimeter (cm) = 10 mm
   - 800 cm = 800 × 10 mm = 8000 mm
   - Total = 8000 mm + 8 mm = 8008 mm

Now, let's arrange these values in decreasing order:
- 8080 mm (80 dm 8 cm)
- 8500 mm
- 8008 mm (800 cm 8 mm)
- 8000 mm (8 m)

Thus, Option 4 correctly arranges the lengths in decreasing order.

**Explanation for Incorrect Options:**

1. **Option 1: 8500 mm, 800 cm 8 mm, 80 dm**
   - 8500 mm = 8500 mm
   - 800 cm 8 mm = 8008 mm
   - 80 dm = 8000 mm
   - Arranged order: 8500 mm, 8008 mm, 8000 mm
   - This is not in decreasing order.

2. **Option 2: 8 cm, 8 m**
   - 8 cm = 80 mm
   - 8 m = 8000 mm
   - Arranged order: 8000 mm, 80 mm
   - This is not in decreasing order.

3. **Option 3: 80 dm 8 cm, 8500 mm, 8 m, 800 cm 8 mm**
   - 80 dm 8 cm = 8080 mm
   - 8500 mm = 8500 mm
   - 8 m = 8000 mm
   - 800 cm 8 mm = 8008 mm
   - Arranged order: 8080 mm, 8500 mm, 8000 mm, 8008 mm
   - This is not in decreasing order.

Therefore, Option 4 is the only option that correctly arranges the lengths in decreasing order.