To solve the problem step by step, we will analyze the work done by A, B, and C, and then find how much less efficient C is compared to A.
### Step 1: Calculate A's Work Rate
A completes 45% of the work in 11 1/4 days.
- Convert 11 1/4 days to an improper fraction:
\( 11 \frac{1}{4} = \frac{45}{4} \) days.
To find A's work rate (work done per day), we use the formula:
\[ \text{Work Rate of A} = \frac{\text{Work Done}}{\text{Time Taken}} \]
\[ \text{Work Rate of A} = \frac{45\%}{\frac{45}{4}} = \frac{45}{\frac{45}{4}} = 4\% \text{ per day} \]
### Step 2: Calculate B's Work Rate
B completes 30% of the work in 3 days.
- Using the same formula for B:
\[ \text{Work Rate of B} = \frac{30\%}{3} = 10\% \text{ per day} \]
### Step 3: Calculate Combined Work Rate of A and B
Now, we can find the combined work rate of A and B:
\[ \text{Combined Work Rate of A and B} = \text{Work Rate of A} + \text{Work Rate of B} \]
\[ = 4\% + 10\% = 14\% \text{ per day} \]
### Step 4: Calculate Work Rate of A, B, and C Together
It is given that A, B, and C together can complete the entire work in \( \frac{1}{64} \) days.
- Therefore, their combined work rate is:
\[ \text{Combined Work Rate of A, B, and C} = \frac{100\%}{\frac{1}{64}} = 6400\% \text{ per day} \]
### Step 5: Calculate C's Work Rate
Now, we can find C's work rate by subtracting the combined work rate of A and B from the total work rate:
\[ \text{Work Rate of C} = \text{Combined Work Rate of A, B, and C} - \text{Combined Work Rate of A and B} \]
\[ = 6400\% - 14\% = 6386\% \text{ per day} \]
### Step 6: Calculate Efficiency Comparison
Now, we need to find how much less efficient C is compared to A:
- A's work rate is \( 4\% \) per day.
- C's work rate is \( 6386\% \) per day.
To find how much less efficient C is than A:
\[ \text{Efficiency Difference} = \text{Efficiency of A} - \text{Efficiency of C} \]
\[ = 4\% - 6386\% \]
Since C is more efficient than A, we can say:
C is not less efficient than A; instead, A is less efficient than C.
### Final Answer
C is more efficient than A, and the difference in efficiency is:
\[ 6386\% - 4\% = 6382\% \]
