NCERT Class XI Mathematics - Sequences and Series - Solutions
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Question : 110
Total: 106
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.
Solution:
Total number of workers = 150
Number of workers on 2nd day = 150 – 4 = 146
Number of workers on 3rd day = 146 – 4 = 142
So, the number of workers will be like 150, 146, 142, .....
Let 150 workers take n days to complete the work, then one worker will complete the work in 150n days. On decreasing the numbers of workers it takes 8 days more to finish the work, then
150 + 146 + 142 + ..... to (n + 8) terms = 150 n
⇒
⇒
⇒ (n + 8) [272 – 4n] = 300 n ⇒ 272n –4 n 2
⇒ –4 n 2 n 2
⇒ (n – 17) (n + 32) = 0 ⇒ n = 17, – 32
n ≠ – 32, because number of days cannot be negative.
∴ n = 17.
So, the work was completed in (17 + 8) i.e., 25 days.
Number of workers on 2nd day = 150 – 4 = 146
Number of workers on 3rd day = 146 – 4 = 142
So, the number of workers will be like 150, 146, 142, .....
Let 150 workers take n days to complete the work, then one worker will complete the work in 150n days. On decreasing the numbers of workers it takes 8 days more to finish the work, then
150 + 146 + 142 + ..... to (n + 8) terms = 150 n
⇒
⇒
⇒ (n + 8) [272 – 4n] = 300 n ⇒ 272n –
⇒ –
⇒ (n – 17) (n + 32) = 0 ⇒ n = 17, – 32
n ≠ – 32, because number of days cannot be negative.
∴ n = 17.
So, the work was completed in (17 + 8) i.e., 25 days.
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