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Misc 32 Important You are here

Last updated at May 29, 2018 by Teachoo

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 = (πππ‘ππ π€πππ)/(ππ’ππππ ππ πππ¦π π‘π πππππππ‘π π€πππ) = 1/π This is the work done by 150 workers Work done by 1 worker in one day = 1/150π Given that In this manner it took 8 more days to finish the work i.e. work finished in (n + 8) days Therefore, 150/150π + 146/150π + 144/150π + β¦ + to (n + 8)term = 1 1/150π [150 + 146 + 142 + β¦ to (n + 8)term]= 1 150 + 146 + 142 + β¦ + to (n + 8)terms = 150n 150 + 146 + 142 + β¦ + to (n + 8) terms this is an AP, where first term (a) = 150 Common difference = 146 β 150 = -4 We know that sum of n terms of AP Sn = π/2[2a + (n β 1)d] Putting n = n + 8 , a = 150 , d = -4 Sn + 8 = (π+8)/2[2(150) + (n + 8 β 1)(-4)] = (π+8)/2 [300 + (n + 7)(-4)] = (π+8)/2 [300 β 4 (n + 7)] = (2(π+8))/2[150 β 2(n + 7)] = (n + 8)[150 β 2(n + 7)] = (n + 8)[150 β 2n β 14] = n(150 β 2n β 14) + 1200 β 16n β 112 = 150n β 2n2 β 14n -16n + 1200 β 112 = β 2n2 + 150n β 14n β 16n + 1200 β 112 = β 2n2 + 120n + 1088 Hence, 150 +146 +142 + β¦ to (n + 8)term = -2n2 + 120n + 1088 Also, we know that 150 +146 +142 + β¦ to (n + 8)term = 150n β 2n2 + 120n + 1088 = 150n β 2n2 + 120n β 150n + 1088 = 0 β 2n2 β 30n + 1088 = 0 2n2 + 30n β 1088 = 0 n2 + 15n β 544 = 0 n2 + 32n β 17n β 544 = 0 n (n + 32) β 17(n + 32) = 0 (n β 17)(n + 32) = 0 Since n cannot be negative , n = β 32 is not possible Hence n = 17 Work was completed in n + 8 days i.e. 17 + 8 = 25 days