# Misc 32 - Chapter 9 Class 11 Sequences and Series (Term 1)

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

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

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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 10 years. He provides courses for Maths and Science at Teachoo.