Radhika purchased one dozen bangles. One day she slipped on the floor fell down. What can not be the ratio of broken is unbroken bangle:

Options

A. `1:2`
B. `1:3`
C. `2:3`
D. `1:5`

Answer

To solve the problem, we need to determine which ratio of broken to unbroken bangles is not possible given that Radhika purchased one dozen (12) bangles.

### Step-by-Step Solution:

1. **Understanding the Total Bangles**:
Radhika purchased 12 bangles in total.

2. **Defining the Ratios**:
We will analyze the four options provided to see which one does not represent a possible scenario of broken to unbroken bangles.

3. **Option 1: Ratio 1:2**
- Total parts = 1 + 2 = 3
- Each part represents \( \frac{12}{3} = 4 \) bangles.
- Broken bangles = 1 part = 4 bangles.
- Unbroken bangles = 2 parts = \( 2 \times 4 = 8 \) bangles.
- This ratio is possible (4 broken, 8 unbroken).

4. **Option 2: Ratio 1:3**
- Total parts = 1 + 3 = 4
- Each part represents \( \frac{12}{4} = 3 \) bangles.
- Broken bangles = 1 part = 3 bangles.
- Unbroken bangles = 3 parts = \( 3 \times 3 = 9 \) bangles.
- This ratio is also possible (3 broken, 9 unbroken).

5. **Option 3: Ratio 2:3**
- Total parts = 2 + 3 = 5
- Each part represents \( \frac{12}{5} = 2.4 \) bangles.
- Broken bangles = 2 parts = \( 2 \times 2.4 = 4.8 \) bangles.
- Unbroken bangles = 3 parts = \( 3 \times 2.4 = 7.2 \) bangles.
- This ratio is not possible since we cannot have a fraction of a bangle.

6. **Option 4: Ratio 1:5**
- Total parts = 1 + 5 = 6
- Each part represents \( \frac{12}{6} = 2 \) bangles.
- Broken bangles = 1 part = 2 bangles.
- Unbroken bangles = 5 parts = \( 5 \times 2 = 10 \) bangles.
- This ratio is possible (2 broken, 10 unbroken).

7. **Conclusion**:
The ratio that cannot represent broken to unbroken bangles is **Option 3: 2:3**.