Understanding Work and Time Problems
This question involves a concept known as inverse proportion. When the amount of work is constant, the number of workers and the time taken to complete the job are inversely related. This means if you increase the number of workers, the time required to finish the job decreases, and vice versa.
Calculating Total Work
First, we need to determine the total amount of work required to complete the job. This is often measured in "worker-days," which represents the total effort needed.
- Number of workers (initial): 4
- Time taken (initial): 12 days
The total work can be calculated as:
Total Work = Number of Workers \(\times\) Time Taken
Total Work = \(4 \text{ workers} \times 12 \text{ days} = 48 \text{ worker-days}\)
Calculating Time for More Workers
Now, we know the total work required is 48 worker-days. We need to find out how many days it will take for 6 workers to complete this same amount of work.
- Total Work: 48 worker-days
- Number of workers (new): 6
- Time taken (new): Let this be '\(D\)' days
Using the same formula for total work:
Total Work = Number of Workers \(\times\) Time Taken
\(48 \text{ worker-days} = 6 \text{ workers} \times D \text{ days}\)
Solving for the Unknown Time
To find the value of '\(D\)', we rearrange the equation:
\(D = \frac{\text{Total Work}}{\text{Number of workers (new)}}\)
\(D = \frac{48 \text{ worker-days}}{6 \text{ workers}}\)
\(D = 8 \text{ days}\)
Conclusion
Therefore, 6 workers will take 8 days to complete the same job.
Similar Questions
- A can do a job in 12 days B in 18 days. A works for 3 days then B joins. Total days to finish?
- If 6 workers complete a job in 15 days. How many days will 9 workers take assuming the same work rate?
- If 4 workers can complete a task in 8 days. How many days will 8 workers take to complete the same task?
- A can do a job in 10 days and B can do it in 15 days. If they work together, how long will it take them to complete the job?
Important Questions from Time and work
A person can complete 20% of work in 8 days and another person y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?
P works thrice as fast as Q, whereas P and Q together can work four times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?
There are three pillars X, Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance, A climbs on X by 6 cm but slips down 1 cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of them requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar?
There is an order of 19000 quantity of a particular product from a customer. The firm produces 1000 quantity of that product per out of which 5% are unfit for sale. In how many days will the order be completed?
Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone?
