After working for 8 days, Anil finds that only `1/3` of the work has been done. He employs Rakesh who is 60% efficient as Anil. How many more days will Anil take to complete the job?

Options

A. 15 days
B. 26.6 days
C. 25 days
D. 20 days

Answer

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

### Step 1: Determine the total work done by Anil in 8 days.
Anil has completed \( \frac{1}{3} \) of the work in 8 days.

### Step 2: Calculate the total work.
If \( \frac{1}{3} \) of the work is done in 8 days, then the total work (W) can be calculated as:
\[ W = 8 \text{ days} \times 3 = 24 \text{ days} \]
This means Anil would take 24 days to complete the entire work alone.

### Step 3: Calculate Anil's daily work efficiency.
Anil’s efficiency can be determined as:
\[ \text{Efficiency of Anil} = \frac{W}{\text{Total days}} = \frac{1}{24} \text{ of the work per day} \]

### Step 4: Determine the remaining work.
Since \( \frac{1}{3} \) of the work is done, the remaining work is:
\[ \text{Remaining work} = 1 - \frac{1}{3} = \frac{2}{3} \]

### Step 5: Calculate Rakesh's efficiency.
Rakesh is 60% as efficient as Anil. Therefore, Rakesh's efficiency is:
\[ \text{Efficiency of Rakesh} = 0.6 \times \frac{1}{24} = \frac{0.6}{24} = \frac{1}{40} \text{ of the work per day} \]

### Step 6: Calculate the total work done by Anil and Rakesh together.
Now, Anil and Rakesh will work together to complete the remaining work. Their combined efficiency is:
\[ \text{Combined efficiency} = \text{Efficiency of Anil} + \text{Efficiency of Rakesh} = \frac{1}{24} + \frac{1}{40} \]
To add these fractions, find a common denominator (which is 120):
\[ \frac{1}{24} = \frac{5}{120}, \quad \frac{1}{40} = \frac{3}{120} \]
Thus,
\[ \text{Combined efficiency} = \frac{5}{120} + \frac{3}{120} = \frac{8}{120} = \frac{1}{15} \text{ of the work per day} \]

### Step 7: Calculate the time taken to complete the remaining work.
To find out how many days it will take to finish the remaining \( \frac{2}{3} \) of the work, we can use the formula:
\[ \text{Time} = \frac{\text{Remaining work}}{\text{Combined efficiency}} = \frac{\frac{2}{3}}{\frac{1}{15}} = \frac{2}{3} \times 15 = 10 \text{ days} \]

### Conclusion:
Anil will take **10 more days** to complete the job with Rakesh's help.

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