Solving the Workers and Days Problem
This question involves a typical work and time scenario where we need to determine how the time taken to complete a job changes when the number of workers changes. We are given information about the time taken by a certain number of workers and asked to find the time taken by a different number of workers for the same job, assuming they all work at the same rate.
Understanding Inverse Proportion
The relationship between the number of workers and the time taken to complete a job is an example of inverse proportion. This means that if you increase the number of workers, the time required to finish the job decreases, and vice versa, provided the amount of work and the rate of work per worker remain constant.
We can express this relationship mathematically:
Number of Workers \(\propto \frac{1}{\text{Number of Days}}\)
Or, alternatively, the total amount of work can be considered constant:
Total Work = (Number of Workers) \(\times\) (Number of Days)
This total work is often measured in "worker-days".
Step-by-Step Calculation
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Calculate Total Work:
First, determine the total effort required to complete the job. This is calculated by multiplying the number of workers by the number of days they took.
Given: 6 workers complete the job in 15 days.
Total Work = \(6 \text{ workers} \times 15 \text{ days}\)
Total Work = \(90 \text{ worker-days}\)
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Calculate Time for New Number of Workers:
Now, use the total work calculated and the new number of workers to find the number of days required. Let '\(D\)' be the number of days the 9 workers will take.
Total Work = (New Number of Workers) \(\times\) (New Number of Days)
\(90 \text{ worker-days} = 9 \text{ workers} \times D \text{ days}\)
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Solve for D:
To find '\(D\)', divide the total work by the new number of workers.
\(D = \frac{90 \text{ worker-days}}{9 \text{ workers}}\)
\(D = 10 \text{ days}\)
Conclusion
Therefore, if 9 workers work on the same job at the same rate, they will complete it in 10 days.
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 4 workers can complete a job in 12 days, how many days will 6 workers take to complete the same job?
- 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?
