The correct ascending order of magnitude, if the ratios `1:2, 2:5 and 3:4` is

Options

A. `2:5lt1:2lt3:4`
B. `1:2lt2:5lt3:4`
C. `3:4lt1:2lt2:5`
D. `1:2lt3:4lt2:5`

Answer

To find the correct ascending order of the ratios \(1:2\), \(2:5\), and \(3:4\), we will convert each ratio into decimal form and then compare their values.

### Step-by-Step Solution:

1. **Convert Ratios to Fractions:**
- The ratios can be expressed as fractions:
- \(1:2\) can be written as \(\frac{1}{2}\)
- \(2:5\) can be written as \(\frac{2}{5}\)
- \(3:4\) can be written as \(\frac{3}{4}\)

2. **Calculate Decimal Values:**
- Now, we will convert these fractions into decimal form:
- \(\frac{1}{2} = 0.5\)
- \(\frac{2}{5} = 0.4\)
- \(\frac{3}{4} = 0.75\)

3. **List the Decimal Values:**
- We have the following decimal values:
- \(\frac{2}{5} = 0.4\)
- \(\frac{1}{2} = 0.5\)
- \(\frac{3}{4} = 0.75\)

4. **Arrange in Ascending Order:**
- Now, we will arrange these decimal values in ascending order (from smallest to largest):
- The smallest value is \(0.4\) (which corresponds to \(\frac{2}{5}\))
- Next is \(0.5\) (which corresponds to \(\frac{1}{2}\))
- The largest value is \(0.75\) (which corresponds to \(\frac{3}{4}\))

5. **Final Ascending Order of Ratios:**
- Therefore, the correct ascending order of the ratios is:
- \(2:5\), \(1:2\), \(3:4\)

### Final Answer:
The correct ascending order of magnitude is \(2:5\), \(1:2\), \(3:4\).

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