Question

A man completes \( \frac{5}{8} \) part of a job in 10 days. At this rate, how many more days will he take to complete the job?

• A. 5
• B. 6
• C. 7
• D. 8

Hint:

Pay close attention to the wording. The question asks for "how many more days," not the "total number of days." This is a common trap in competitive exams.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a work and time problem. We first need to find the total time required to complete the job and then find the remaining time.
Step 2: Key Formula or Approach:
If a fraction of work is done in a certain time, we can calculate the time needed for the remaining fraction of work.
Step 3: Detailed Explanation:
Method 1: Find total time first
The man completes \( \frac{5}{8} \) of the job in 10 days.
To find the time to complete the whole job (1 job), we can set up a proportion:
\[ \text{Time for whole job} = \frac{\text{Days taken}}{\text{Fraction of work done}} = \frac{10}{\frac{5}{8}} = 10 \times \frac{8}{5} = 2 \times 8 = 16 \text{ days} \] The total time to complete the job is 16 days.
He has already worked for 10 days.
\[ \text{More days needed} = \text{Total time} - \text{Time worked} = 16 - 10 = 6 \text{ days} \] Method 2: Calculate remaining work
Fraction of work completed = \( \frac{5}{8} \)
Fraction of work remaining = \( 1 - \frac{5}{8} = \frac{3}{8} \)
We know that \( \frac{5}{8} \) of the work takes 10 days.
Let's find the time taken for \( \frac{1}{8} \) of the work:
\[ \text{Time for } \frac{1}{8} \text{ work} = \frac{10 \text{ days}}{5} = 2 \text{ days} \] Now, calculate the time for the remaining \( \frac{3}{8} \) of the work:
\[ \text{Time for } \frac{3}{8} \text{ work} = 3 \times (\text{Time for } \frac{1}{8} \text{ work}) = 3 \times 2 = 6 \text{ days} \] Step 4: Final Answer:
The man will take 6 more days to complete the job.