'A' can complete a work in 20 days while B is `25%` more efficient than A. B worked for 6 days and left. The remaining work is completed by Cin 15 days. Find in how many days C can complete the whole work alone.

Options

A. 27 days
B. 21 days
C. 18 days
D. 24 days

Answer

To solve the problem, we need to determine how many days C can complete the whole work alone. Let's break down the solution step by step.

### Step 1: Determine A's work rate
A can complete the work in 20 days. Therefore, A's work rate is:
\[ \text{Work rate of A} = \frac{1}{20} \text{ (work per day)} \]

### Step 2: Determine B's work rate
B is 25% more efficient than A. To find B's work rate, we first calculate 25% of A's work rate:
\[ 25\% \text{ of A's work rate} = 0.25 \times \frac{1}{20} = \frac{1}{80} \]
Now, we add this to A's work rate to find B's work rate:
\[ \text{Work rate of B} = \frac{1}{20} + \frac{1}{80} \]
To add these fractions, we need a common denominator, which is 80:
\[ \text{Work rate of B} = \frac{4}{80} + \frac{1}{80} = \frac{5}{80} = \frac{1}{16} \text{ (work per day)} \]

### Step 3: Calculate the work done by B in 6 days
Now, we calculate how much work B completes in 6 days:
\[ \text{Work done by B in 6 days} = 6 \times \frac{1}{16} = \frac{6}{16} = \frac{3}{8} \]

### Step 4: Determine the remaining work
The total work is considered as 1 unit. Therefore, the remaining work after B has worked for 6 days is:
\[ \text{Remaining work} = 1 - \frac{3}{8} = \frac{5}{8} \]

### Step 5: Calculate C's work rate
C completes the remaining work in 15 days. Therefore, C's work rate can be calculated as:
\[ \text{Work rate of C} = \frac{\text{Remaining work}}{\text{Time taken by C}} = \frac{\frac{5}{8}}{15} = \frac{5}{120} = \frac{1}{24} \text{ (work per day)} \]

### Step 6: Determine how many days C can complete the whole work alone
To find out how many days C can complete the whole work alone, we take the reciprocal of C's work rate:
\[ \text{Days taken by C to complete the whole work} = \frac{1}{\frac{1}{24}} = 24 \text{ days} \]

### Final Answer
C can complete the whole work alone in **24 days**.