Question
Arjun can finish 60% of a job in 9 days. Bittu needs 9
more days than Arjun to finish the whole job, and Bittu’s efficiency is 25% higher than Charu’s. The work starts with Arjun alone. On the 2nd day, Arjun works with Bittu only. On the 3rd day, Arjun works with Charu only. On the 4th day, Arjun works alone again. This cycle continues in the same pattern for 9 days. What is the percentage difference between the sum of the times Arjun alone and Bittu alone would take to finish the remaining work, compared to the time Charu alone would take?Solution
ATQ, Let the Arjun, Bittu and Charu can be defined as A, B and C respectively
A can finish the work in 9 ÷ 0.6 = 15 days. B’s time to complete the work is 15 + 9 = 24 days. C alone would take 24 × 1.25 = 30 days. Assume the total work is 600 units. Efficiency of A = 600 ÷ 15 = 40 units/day. Efficiency of B = 600 ÷ 24 = 25 units/day. Efficiency of C = 600 ÷ 30 = 20 units/day. In 3 days, the combined work done is: 40 + 40 + 25 + 40 + 20 = 165 units. In 9 days, they complete 165 × 3 = 495 units. Remaining work = 600 − 495 = 105 units. If A works alone, time to finish the rest = 105 ÷ 40 = 2.625 days. If B works alone, time = 105 ÷ 25 = 4.2 days. If C works alone, time = 105 ÷ 20 = 5.25 days. Required percentage = [(2.625 + 4.2 − 5.25) ÷ 5.25] × 100 = 30%.
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