Question
A man takes 200 days to finish a work alone. If he
started working alone and joined by one more man having same efficiency as of him every day from 2nd day onwards, then find the time taken to finish the same work this way.Solution
ATQ, Let the total work be 200x units Efficiency of each man = (200x / 200) = x units/day Total time taken = {n × (n + 1)} ÷ 2 = 200 So, n × (n + 1) = 400 Or, n² + n = 400 Or, n² + n – 400 = 0 Or, n² + 21n – 20n – 400 = 0 Or, n(n + 21) – 20(n + 21) = 0 Or, (n – 20)(n + 21) = 0 So, n = 20 Number of days required to finish the work = 20
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