36
To solve this problem, we can use the concept of man-hours, a common technique in work and time problems. This approach calculates the total hours required to complete a job based on the number of workers and hours worked per day.
First, determine the volume of the wall that 12 men can build.
- Volume of original wall = Length × Breadth × Height
\(= 100 \, \text{m} \times 0.2 \, \text{m} \times 5 \, \text{m} = 100 \times 0.2 \times 5 = 100 \, \text{m}^3\)
Next, find out the total man-hours required to build the wall, given the current team configuration:
- Total man-hours = (Number of workers) × (Hours per day) × (Days)
\(= 12 \times 8 \times 10 = 960 \, \text{man-hours}\)
To build this wall, 960 man-hours are required. Now, calculate the volume of the new wall:
- Volume of new wall = Length × Breadth × Height
\(= 200 \, \text{m} \times 0.6 \, \text{m} \times 5 \, \text{m} = 600 \, \text{m}^3\)
The ratio of volumes gives us the ratio of man-hours needed:
- Volume Ratio = \(\frac{600}{100} = 6\)
Thus, the man-hours required for the new wall is:
- Total man-hours for new wall = 960 × 6 = 5760 man-hours
Now calculate how many days 16 men working 10 hours a day will take to complete this:
- Work done per day by 16 men = (Number of workers) × (Hours per day)
Work done per day = \(16 \times 10 = 160 \, \text{man-hours}\) - Days required = \(\frac{5760}{160} = 36 \, \text{days}\)
Thus, the correct answer is: 36 days.
Similar Questions
- A, B, C, D can complete a work in 3, 6, 9, 12 hours respectively. Further, only one person can work at a time in each hour and nobody can work for two consecutive hours. It is not necessary to engage all. What is the minimum number of hours that they will take to finish the work?
- 50 men can complete a work in 40 days. They begin the work together but a batch of 5 men left after each period of 10 days. What is the time to complete the work?
- If the work done by \(x\) men in \((x + 1)\) days is equal to the work done by \((x + 5)\) men in \((x - 2)\) days, then what is the value of \(x\)?
- \(p\) number of men can finish a piece of work in \(q\) days. If there are 50% more men, then the work will be finished 12 days earlier. What is the value of \(q\)?
- Eight men and 24 women can finish a piece of work in one day while 12 men and 18 women can also finish it in one day. What is the time taken by 24 men and 72 women to finish the work ?
- X can do a piece of work in 4 days and Y can do the same piece of work in 6 days. Which of the following statements is/are correct ?
I. If X and Y work alternately starting with X, then the piece of work will be finished on the fifth day.
II. If X and Y work alternately starting with Y, then the piece of work will be finished in less than 5 days.
Select the answer using the code given below :
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?
