Understanding the Work and Time Problem
This question is about calculating the time required to complete a piece of work when the number of workers changes. We are given that a certain number of men (\(p\)) can finish a work in \(q\) days. The scenario changes when the number of men increases, and the work gets completed faster. We need to find the original number of days (\(q\)) required.
Let's break down the information:
- Initial number of men = \(p\)
- Initial number of days = \(q\)
- Total work done is proportional to the number of men multiplied by the number of days. So, Total Work = \(p \times q\).
Now, consider the change:
- The number of men increases by 50%.
- New number of men = Initial men + 50% of Initial men
- New number of men = \(p + 0.50 \times p = 1.5p\)
- The work is finished 12 days earlier.
- New number of days = Initial days - 12 days = \(q - 12\)
Since the amount of work remains the same, the total work done initially must equal the total work done with the increased number of men.
Calculating the Value of q
We can set up an equation based on the principle that Work = Number of Men × Number of Days:
Initial Work = New Work
\(p \times q = (1.5p) \times (q - 12)\)
Now, we solve this equation for \(q\). Since \(p\) represents the number of men, we know \(p\) cannot be zero. Therefore, we can divide both sides of the equation by \(p\):
\(q = 1.5 \times (q - 12)\)
Let's simplify the equation:
- Distribute the 1.5 on the right side:
\(q = 1.5q - (1.5 \times 12)\)
\(q = 1.5q - 18\)
- Now, we need to isolate \(q\). Subtract \(q\) from both sides:
\(0 = 1.5q - q - 18\)
\(0 = 0.5q - 18\)
- Add 18 to both sides:
\(18 = 0.5q\)
- To find \(q\), divide 18 by 0.5:
\(q = \frac{18}{0.5}\)
\(q = 18 \times 2\)
\(q = 36\)
Conclusion
The initial number of days (\(q\)) required for \(p\) men to finish the work is 36 days.
Therefore, the value of \(q\) is 36.
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 \(x\)?
- 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 : - 12 men working 8 hours a day can completely build a wall of length 100 m, breadth 20 cm and height 5 m in 10 days. How many days will 16 men working 10 hours a day require to build a wall of length 200 m, breadth 60 cm and height 5 m ?
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?
