Following are the questions based on two statements and answer the following based on the given statements.
C alone can complete the work in 15 days. In what time C and A together can complete the whole work.
Statement I. A is 25% more efficient than B and B alone can complete the work in 20 days
Statement II. Difference between the time taken by A alone and B alone to complete the work is 22 days , and time taken by C alone to finish the work is 10% more than the time taken by A and B together to complete the work.

Options

A. Statement I alone is sufficient to answer the question while statement II alone is not sufficient to answer the question
B. tatement II alone is sufficient to answer the question while statement I alone is not sufficient to answer the question
C. Both statements I and II together are required to tedes answer the question.
D. Either the statement I alone or Statement II alone Vis sufficient to answer the question

Answer

To solve the problem, we need to determine how long A and C together will take to complete the work, given the information from the two statements.

### Step-by-Step Solution:

1. **Understanding the Work Rates**:
- C can complete the work alone in 15 days. Therefore, C's work rate is:
\[ \text{Work rate of C} = \frac{1}{15} \text{ (work/day)} \]

2. **Analyzing Statement I**:
- A is 25% more efficient than B, and B can complete the work in 20 days.
- B's work rate is:
\[ \text{Work rate of B} = \frac{1}{20} \text{ (work/day)} \]
- Since A is 25% more efficient than B, we can calculate A's work rate as follows:
\[ \text{Efficiency of A} = \text{Efficiency of B} \times 1.25 \]
\[ \text{Work rate of A} = \frac{1}{20} \times 1.25 = \frac{1.25}{20} = \frac{1}{16} \text{ (work/day)} \]

3. **Calculating Combined Work Rate of A and C**:
- Now, we can find the combined work rate of A and C:
\[ \text{Combined work rate of A and C} = \text{Work rate of A} + \text{Work rate of C} \]
\[ = \frac{1}{16} + \frac{1}{15} \]
- To add these fractions, we need a common denominator. The least common multiple (LCM) of 16 and 15 is 240.
\[ \frac{1}{16} = \frac{15}{240}, \quad \frac{1}{15} = \frac{16}{240} \]
\[ \text{Combined work rate} = \frac{15}{240} + \frac{16}{240} = \frac{31}{240} \text{ (work/day)} \]

4. **Calculating Time Taken by A and C Together**:
- The time taken by A and C together to complete the work is the reciprocal of their combined work rate:
\[ \text{Time} = \frac{1}{\text{Combined work rate}} = \frac{240}{31} \text{ days} \]

5. **Conclusion**:
- A and C together can complete the work in \(\frac{240}{31}\) days.