What is the ratio of ATP requirement for the fixation of 6 molecules of `CO_2` in sugarcane and 5 molecules of `N_2` in bean ?

Options

A. `9 : 40`
B. `3 : 16`
C. `5 : 8 `
D. `3 : 8 `

Answer

To solve the problem of determining the ratio of ATP requirement for the fixation of 6 molecules of CO2 in sugarcane and 5 molecules of N2 in beans, we can follow these steps:

### Step-by-Step Solution:

1. **Understand ATP Requirement for CO2 Fixation in Sugarcane**:
- For the fixation of 3 molecules of CO2, the requirement is 9 ATP molecules.
- Therefore, for 6 molecules of CO2 (which is double), the ATP requirement will be:
\[ \text{ATP for 6 CO2} = 9 \, \text{ATP} \times 2 = 18 \, \text{ATP} \]

2. **Understand ATP Requirement for N2 Fixation in Beans**:
- For the fixation of 1 molecule of N2, the requirement is 16 ATP molecules.
- Therefore, for 5 molecules of N2, the ATP requirement will be:
\[ \text{ATP for 5 N2} = 16 \, \text{ATP} \times 5 = 80 \, \text{ATP} \]

3. **Calculate the Ratio of ATP Requirements**:
- Now we need to find the ratio of ATP required for CO2 fixation to that required for N2 fixation:
\[ \text{Ratio} = \frac{\text{ATP for 6 CO2}}{\text{ATP for 5 N2}} = \frac{18}{80} \]

4. **Simplify the Ratio**:
- To simplify the ratio \( \frac{18}{80} \):
\[ \frac{18}{80} = \frac{9}{40} \]

5. **Final Answer**:
- The ratio of ATP requirement for the fixation of 6 molecules of CO2 in sugarcane to the fixation of 5 molecules of N2 in beans is \( 9:40 \).

### Conclusion:
The correct answer is \( 9:40 \).