Question 32 150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.
Class X1 - Maths -Sequences and Series Page 200
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Let n is the number of days in which work is completed. according to question 4 workers dropped on everyday . hence,the number of workers is 150, 146, 142 , 138, ..........
first term = 150
common difference = 146 - 150 = -4
hence, the number of workers would have worked for all the n days = Sₙ
= n/2{ 2 × 150 + ( n - 1) × ( - 4) }
Had the workers not dropped then work would have finished in ( n - 8) days with 150 workers working on each day .Hence, the number of workers would have worked for all the n days is 150(n - 8) .
it is clear that work on both conditions is same.
150( n - 8 ) = n/2[ 2 × 150 + ( n - 1) × (-4)]
150n - 1200 = 150n -2n² + 2n
2n² - 2n - 1200 = 0
n² - n - 600 = 0
n² - 25n + 24n - 600 = 0
n( n - 25) + 24( n - 25) = 0
(n - 25)( n + 24) = 0
n = -24 , 25 , n ≠ -1
hence, work will be completed in 25 days .
first term = 150
common difference = 146 - 150 = -4
hence, the number of workers would have worked for all the n days = Sₙ
= n/2{ 2 × 150 + ( n - 1) × ( - 4) }
Had the workers not dropped then work would have finished in ( n - 8) days with 150 workers working on each day .Hence, the number of workers would have worked for all the n days is 150(n - 8) .
it is clear that work on both conditions is same.
150( n - 8 ) = n/2[ 2 × 150 + ( n - 1) × (-4)]
150n - 1200 = 150n -2n² + 2n
2n² - 2n - 1200 = 0
n² - n - 600 = 0
n² - 25n + 24n - 600 = 0
n( n - 25) + 24( n - 25) = 0
(n - 25)( n + 24) = 0
n = -24 , 25 , n ≠ -1
hence, work will be completed in 25 days .
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