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150 workers were engaged to finish a piece of work in certain number of days 4 workers left on the second day, 4 more workers left on-third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed. I need the answer with steps well xplained?
Verified Answer
150 workers were engaged to finish a piece of work in certain number o...
let the work be complete in x days
The work should have been complete by x-8 days.
Total man-days= 150(x-8)
As four worker drop on each day
The total work days are 150,150-4, 150-8..... 150-(x-1)4
These are in arithmetic progression where
a1=150 d= - 4 and n=x
so total working man-days= x(2a1-4(x-1))/2
= x(300-4x+4)/2
Then we have 150(x-8)=x(304-4x)/2
⇒ 300x-2400= 304x-4x^2
⇒ 75x-600=76x-x^2
⇒ x^2 -x -600=0
⇒ (x-25)(x+24)=0
solving we have x=25
The work was complete in 25 days.
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Most Upvoted Answer
150 workers were engaged to finish a piece of work in certain number o...
Initial Situation:
150 workers were engaged to finish a piece of work in a certain number of days.
Workers Leaving:
- On the second day, 4 workers left.
- On the third day, 4 more workers left.
- This pattern continues, with 4 workers leaving each subsequent day.
Effect of Workers Leaving:
The number of workers decreases each day, which means the productivity of the workers also decreases. As a result, more time is required to finish the work.
Additional Time Required:
It takes 8 more days to finish the work after workers start leaving.
Finding the Number of Days:
To find the number of days it takes to finish the work, we can work backwards from the additional time required.
- Let's assume the work was completed in 'x' days initially.
- After 1 day, the remaining workers would have worked for (x-1) days.
- After the second day, the remaining workers would have worked for (x-2) days.
- This pattern continues until the last day when only 4 workers are left, and they would have worked for (x - (x-1) - (x-2) - ... - 4) days.
Total Work Done:
The total work done by all the workers can be calculated by summing up the work done individually by each group of workers.
- The initial 150 workers worked for 'x' days, so they completed 150x units of work.
- The 4 workers who left on the second day worked for (x-1) days, so they completed 4(x-1) units of work.
- The 4 workers who left on the third day worked for (x-2) days, so they completed 4(x-2) units of work.
- This pattern continues until the last group of 4 workers who worked for (x - (x-1) - (x-2) - ... - 4) days and completed 4(x - (x-1) - (x-2) - ... - 4) units of work.
Total Work Equation:
The total work completed by all the workers can be expressed as the sum of the work done by each group:
150x + 4(x-1) + 4(x-2) + ... + 4(x - (x-1) - (x-2) - ... - 4)
Simplifying the Equation:
By simplifying the equation, we can find the value of 'x' and determine the number of days it took to complete the work.
150x + 4(x-1) + 4(x-2) + ... + 4(x - (x-1) - (x-2) - ... - 4) = 150x + 4(x-1) + 4(x-2) + ... + 4(4)
150x + 4x(x-1)/2 = 150x + 4(4)
150x + 2x(x-1) = 150x + 16
150x + 2x^2 - 2x = 150x + 16
2x^2 - 2x - 16 = 0
x^2 - x - 8 = 0
(x - 4)(x + 2) = 0
x = 4 or x = -2
150 workers were engaged to finish a piece of work in a certain number of days.
Workers Leaving:
- On the second day, 4 workers left.
- On the third day, 4 more workers left.
- This pattern continues, with 4 workers leaving each subsequent day.
Effect of Workers Leaving:
The number of workers decreases each day, which means the productivity of the workers also decreases. As a result, more time is required to finish the work.
Additional Time Required:
It takes 8 more days to finish the work after workers start leaving.
Finding the Number of Days:
To find the number of days it takes to finish the work, we can work backwards from the additional time required.
- Let's assume the work was completed in 'x' days initially.
- After 1 day, the remaining workers would have worked for (x-1) days.
- After the second day, the remaining workers would have worked for (x-2) days.
- This pattern continues until the last day when only 4 workers are left, and they would have worked for (x - (x-1) - (x-2) - ... - 4) days.
Total Work Done:
The total work done by all the workers can be calculated by summing up the work done individually by each group of workers.
- The initial 150 workers worked for 'x' days, so they completed 150x units of work.
- The 4 workers who left on the second day worked for (x-1) days, so they completed 4(x-1) units of work.
- The 4 workers who left on the third day worked for (x-2) days, so they completed 4(x-2) units of work.
- This pattern continues until the last group of 4 workers who worked for (x - (x-1) - (x-2) - ... - 4) days and completed 4(x - (x-1) - (x-2) - ... - 4) units of work.
Total Work Equation:
The total work completed by all the workers can be expressed as the sum of the work done by each group:
150x + 4(x-1) + 4(x-2) + ... + 4(x - (x-1) - (x-2) - ... - 4)
Simplifying the Equation:
By simplifying the equation, we can find the value of 'x' and determine the number of days it took to complete the work.
150x + 4(x-1) + 4(x-2) + ... + 4(x - (x-1) - (x-2) - ... - 4) = 150x + 4(x-1) + 4(x-2) + ... + 4(4)
150x + 4x(x-1)/2 = 150x + 4(4)
150x + 2x(x-1) = 150x + 16
150x + 2x^2 - 2x = 150x + 16
2x^2 - 2x - 16 = 0
x^2 - x - 8 = 0
(x - 4)(x + 2) = 0
x = 4 or x = -2
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150 workers were engaged to finish a piece of work in certain number of days 4 workers left on the second day, 4 more workers left on-third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed. I need the answer with steps well xplained?
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150 workers were engaged to finish a piece of work in certain number of days 4 workers left on the second day, 4 more workers left on-third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed. I need the answer with steps well xplained? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 150 workers were engaged to finish a piece of work in certain number of days 4 workers left on the second day, 4 more workers left on-third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed. I need the answer with steps well xplained? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 150 workers were engaged to finish a piece of work in certain number of days 4 workers left on the second day, 4 more workers left on-third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed. I need the answer with steps well xplained?.
150 workers were engaged to finish a piece of work in certain number of days 4 workers left on the second day, 4 more workers left on-third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed. I need the answer with steps well xplained? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 150 workers were engaged to finish a piece of work in certain number of days 4 workers left on the second day, 4 more workers left on-third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed. I need the answer with steps well xplained? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 150 workers were engaged to finish a piece of work in certain number of days 4 workers left on the second day, 4 more workers left on-third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed. I need the answer with steps well xplained?.
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