Question
Pawan and Qureshi can complete a
task in 12 days, while Pawan and Rishi can finish the same task in 40/3 days. Initially, Pawan and Rishi begin working together. After 4 days, Qureshi joins them. All three work together for the next 6 days, after which Qureshi and Rishi leave the job. The remaining work is finished by Pawan alone in 1 day.Determine the time required for Qureshi, working alone, to complete the entire task.Solution
ATQ,
Let, total work be LCM of 12 and 40/3 = 120 units Units of work done by Pawan and Qureshi together in a day = 120/12 = 10 units Units of work done by Pawan and Rishi together in a day = 120/(40/3) = 9 units Let, units of work done by Qureshi alone in a day = ‘x’ units So, 9 × 4 + (9 + x) × 6 + (10 – x) × 1 = 120 36 + 54 + 6x + 10 – x = 120 5x = 20 x = 4 So, time taken by Qureshi alone to do the work = 120/4 = 30 days
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