Calculating Work Time for 16 Men
This problem involves calculating the time required to complete a task based on the number of workers and the amount of work.
Understanding the Work-Time Relationship
The total amount of work done is directly proportional to the number of men working and the number of days they work. We can express this relationship using the formula:
$Work = (Number of Men) × (Number of Days)$
Or, more generally, for two different scenarios:
$ \frac{M_1 \times D_1}{W_1} = \frac{M_2 \times D_2}{W_2} $
Where:
- \( M_1 \) = Number of men in the first scenario
- \( D_1 \) = Number of days in the first scenario
- \( W_1 \) = Amount of work in the first scenario
- \( M_2 \) = Number of men in the second scenario
- \( D_2 \) = Number of days in the second scenario (to be calculated)
- \( W_2 \) = Amount of work in the second scenario
Applying the Formula to the Problem
We are given:
- \( M_1 = 35 \) men
- \( D_1 = 8 \) days
- \( W_1 = 1 \) unit of work (the original piece of work)
- \( M_2 = 16 \) men
- \( W_2 = 4 \) units of work (four times the original work)
We need to find \( D_2 \).
Step-by-Step Calculation
- Substitute the known values into the formula:
$ \frac{35 \times 8}{1} = \frac{16 \times D_2}{4} $
- Calculate the left side of the equation:
$ 280 = \frac{16 \times D_2}{4} $
- Simplify the right side of the equation:
$ 280 = 4 \times D_2 $
- Solve for \( D_2 \) by dividing both sides by 4:
$ D_2 = \frac{280}{4} $
$ D_2 = 70 $
Therefore, 16 men will require 70 days to do four times the work.
Conclusion
The time required by 16 men to do four times the work is 70 days.
Similar Questions
- A contractor employs 15 men to complete a work in 24 days, working 8 hours per day. After six days, he adds five more men but also reduces the working hours to six per day from the seventh day onwards. If all men work with the same efficiency throughout, how many more days will be required to finish the remaining work?
- 6 women and 4 men can complete a work in 10 days, while 4 women and 5 men complete it in 10 days. In how many days will 8 women complete it?
- If 5 cats can catch 5 mice in 5 minutes, how many cats are needed to catch 100 mice in 100 min?
- A group of 5 men or 12 women can complete a task in 70 days. Find the time taken by 5 men and 12 women to complete the task.
- Athar can do a certain work in the same time in which Baban and Chetan together can do it. If Athar and Baban together could do it in 10 days and Chetan alone in 50 days, then Baban alone could do it in:
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- 66 women can do a piece of work in 79 days. Find the number of days required by 6 women to complete 1 / 11th of the work.
- A, B, and C together can complete a task in 6 days. If A alone takes 12 days and B alone takes 18 days, how long will C alone take?
- A can complete a task in 15 days, and B can complete the same task in 20 days. How long will it take them to complete the task together?
- If 15 boys can build a house in 20 days, in how many days can 20 boys complete the same work.
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?
