Work and Time Calculation: Days for 6 Persons
Problem Setup
The problem involves calculating the time required for a different number of people to complete the same task. This is a typical inverse proportion scenario, where fewer people will take more time.
We are given:
- Initial number of persons ($P_1$): 24
- Initial time taken ($D_1$): 5 days
- Final number of persons ($P_2$): 6
- Final time taken ($D_2$): To be calculated
Inverse Proportion Concept
In problems like this, the total amount of work is constant. The relationship between the number of persons and the number of days is inversely proportional. This means if the number of persons decreases, the number of days required increases proportionally.
The formula for inverse proportion is:
$P_1 \times D_1 = P_2 \times D_2$Solution Steps
- Substitute the known values into the formula:
$24 \times 5 = 6 \times D_2$
- Calculate the total work units:
$120 = 6 \times D_2$
- Solve for the final number of days ($D_2$):
$D_2 = \frac{120}{6}$
$D_2 = 20$
Conclusion
Therefore, 6 persons would be able to complete the task in 20 days.
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Important Questions from Time and Work
A and B can do a piece of work in 18 days. B and C together can do it in 30 days. If A is twice as good a workman as C, find in how many days B alone can do the work?
Two men and 7 women can complete a work in 28 days, whereas 6 men and 16 women can do the same work in 11 days. In how many days will 5 men and 4 women, working together, complete the same work?
A man and a woman, working together can do a work in 66 days. The ratio of their working efficiencies is 3 ∶ 2. In how many days 6 men and 2 women together can do the same work?
Each one of five men independently can complete a work in 20 days. The work is started by one person. Next day one more person joins and every next day one more person joins. From the fifth day, five persons continued working as a team. In how many days, will the work be completed?
Numan does half the work as Gagan in 4/5 of the time. If together they take 16 days to complete a piece of work, then how long will it take Gagan to complete the work?
