Question
David can complete a work alone in 30 days, while Ethan
can complete the same work in 50 days. Both of them started the work together and worked till 96% of the work is completed and then David left the work. If the remaining work is done by Ethan alone, then find the time taken to complete the whole work.Solution
ATQ, Let the total work = 300 units (L.C.M of 30 and 50 units) Efficiency of David = 300/30 = 10 units/day Efficiency of Ethan = 300/50 = 6 units/day 96% of the work = 0.96 × 300 = 288 units Number of days taken by David and Ethan to complete 288 units = 288/(10 + 6) = 18 days Remaining work = 300 – 288 = 12 units Number of days taken by Ethan to complete 12 units of the work = 12/6 = 2 days Total time taken to complete the work = 18 + 2 = 20 days
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