A can do piece of work in 6 days. B is 25% more than efficient than A. How long would B alone take to finish this work?

Options

A. `2 2/3` days
B. `4 4/5` days
C. `3 1/3` days
D. `5 1/4` days

Explanation

To solve the problem, let's break it down step by step.

### Step 1: Determine A's Work Rate
A can complete the work in 6 days. Therefore, A's work rate is:
\[ \text{Work rate of A} = \frac{1 \text{ work}}{6 \text{ days}} = \frac{1}{6} \text{ work per day} \]

### Step 2: Calculate B's Work Rate
B is 25% more efficient than A. To find B's work rate, we first need to calculate 25% of A's work rate:
\[ 25\% \text{ of A's work rate} = 0.25 \times \frac{1}{6} = \frac{0.25}{6} = \frac{1}{24} \]
Now, we add this to A's work rate to find B's work rate:
\[ \text{Work rate of B} = \text{Work rate of A} + 25\% \text{ of A's work rate} = \frac{1}{6} + \frac{1}{24} \]
To add these fractions, we need a common denominator. The least common multiple of 6 and 24 is 24:
\[ \frac{1}{6} = \frac{4}{24} \]
Now we can add:
\[ \text{Work rate of B} = \frac{4}{24} + \frac{1}{24} = \frac{5}{24} \text{ work per day} \]

### Step 3: Calculate the Time Taken by B to Complete the Work
To find out how long B would take to finish the work alone, we take the reciprocal of B's work rate:
\[ \text{Time taken by B} = \frac{1 \text{ work}}{\text{Work rate of B}} = \frac{1}{\frac{5}{24}} = \frac{24}{5} \text{ days} \]
This can be simplified to:
\[ \frac{24}{5} = 4.8 \text{ days} \]

### Final Answer
B alone would take **4.8 days** to finish the work.

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