Question
M, N and O can complete a task in ‘t’, 100, and ‘t
+ 20’ days respectively. All three started together, but after 15 days, N dropped out. Then, 30 days before the work finished, M also left. The work was finished in 60 days. Find the value of ‘t’.Solution
ATQ,
M worked for 30 days, N worked for 15 days and O worked for 60 days So according to question: (30/t) + (15/100) + (60/(t + 20)) = 1 → (30/t) + (60/(t+20)) = 1 – (3/20) → (30t + 600 + 60t)/(t² + 20t) = 17/20 → 17t² + 340t = 600t + 12000 → 17t² – 260t – 12000 = 0 → 17t² – 340t + 80t – 12000 = 0 → 17t(t – 20) + 80(t – 20) = 0 → (17t + 80)(t – 20) = 0 → t = 20 (valid), t = -80/17 (not valid)
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