A man completes 5/8 of a job in 10 days. At this rate, how many more days will it take him to finish the job?

Options

A. 5
B. 6
C. 7
D. `7(1)/(2)`

Answer

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step 1: Understand the total work done
The man completes \( \frac{5}{8} \) of a job in 10 days. We can assume the total work to be 1 unit.

### Step 2: Calculate the time taken to complete the whole job
If \( \frac{5}{8} \) of the job takes 10 days, we can find out how long it would take to complete the entire job (1 unit) using the formula:
\[ \text{Total time for 1 unit} = \text{Time taken for } \frac{5}{8} \text{ of the job} \times \frac{1 \text{ unit}}{\frac{5}{8} \text{ unit}} \]
This simplifies to:
\[ \text{Total time for 1 unit} = 10 \text{ days} \times \frac{8}{5} = 16 \text{ days} \]

### Step 3: Determine the remaining work
The remaining work to be done is:
\[ \text{Remaining work} = 1 - \frac{5}{8} = \frac{3}{8} \text{ of the job} \]

### Step 4: Calculate the time to finish the remaining work
Now, we need to find out how many days it will take to complete the remaining \( \frac{3}{8} \) of the job. Since we know that the entire job takes 16 days, we can set up the equation:
\[ \text{Time for } \frac{3}{8} \text{ of the job} = \frac{3}{8} \times 16 \text{ days} \]
Calculating this gives:
\[ \text{Time for } \frac{3}{8} \text{ of the job} = \frac{3 \times 16}{8} = \frac{48}{8} = 6 \text{ days} \]

### Conclusion
Thus, the man will take **6 more days** to finish the job.

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