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Last updated at May 29, 2018 by Teachoo

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Misc 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. Let total work = 1 and let total work be completed in = n days Work done in 1 day = (๐๐๐ก๐๐ ๐ค๐๐๐)/(๐๐ข๐๐๐๐ ๐๐ ๐๐๐ฆ๐ ๐ก๐ ๐๐๐๐๐๐๐ก๐ ๐ค๐๐๐) = 1/๐ This is the work done by 150 workers Work done by 1 worker in one day = 1/150๐ Given that In this manner it took 8 more days to finish the work i.e. work finished in (n + 8) days Therefore, 150/150๐ + 146/150๐ + 144/150๐ + โฆ + to (n + 8)term = 1 1/150๐ [150 + 146 + 142 + โฆ to (n + 8)term]= 1 150 + 146 + 142 + โฆ + to (n + 8)terms = 150n 150 + 146 + 142 + โฆ + to (n + 8) terms this is an AP, where first term (a) = 150 Common difference = 146 โ 150 = -4 We know that sum of n terms of AP Sn = ๐/2[2a + (n โ 1)d] Putting n = n + 8 , a = 150 , d = -4 Sn + 8 = (๐+8)/2[2(150) + (n + 8 โ 1)(-4)] = (๐+8)/2 [300 + (n + 7)(-4)] = (๐+8)/2 [300 โ 4 (n + 7)] = (2(๐+8))/2[150 โ 2(n + 7)] = (n + 8)[150 โ 2(n + 7)] = (n + 8)[150 โ 2n โ 14] = n(150 โ 2n โ 14) + 1200 โ 16n โ 112 = 150n โ 2n2 โ 14n -16n + 1200 โ 112 = โ 2n2 + 150n โ 14n โ 16n + 1200 โ 112 = โ 2n2 + 120n + 1088 Hence, 150 +146 +142 + โฆ to (n + 8)term = -2n2 + 120n + 1088 Also, we know that 150 +146 +142 + โฆ to (n + 8)term = 150n โ 2n2 + 120n + 1088 = 150n โ 2n2 + 120n โ 150n + 1088 = 0 โ 2n2 โ 30n + 1088 = 0 2n2 + 30n โ 1088 = 0 n2 + 15n โ 544 = 0 n2 + 32n โ 17n โ 544 = 0 n (n + 32) โ 17(n + 32) = 0 (n โ 17)(n + 32) = 0 Since n cannot be negative , n = โ 32 is not possible Hence n = 17 Work was completed in n + 8 days i.e. 17 + 8 = 25 days

Miscellaneous

Misc 1

Misc 2

Misc 3 Important

Misc 4

Misc 5

Misc 6

Misc 7 Important

Misc 8

Misc 9

Misc 10

Misc 11

Misc 12

Misc 13

Misc 14

Misc 15

Misc 16 Important

Misc 17

Misc 18

Misc 19 Important

Misc 20

Misc 21

Misc 22

Misc 23

Misc 24

Misc 25 Important

Misc 26

Misc 27

Misc 28 Important

Misc 29

Misc 30

Misc 31

Misc 32 Important You are here

Chapter 9 Class 11 Sequences and Series

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.