Question
"Arjun" can complete a task on
his own in 20 days. "Bhuvan" requires 5 days more than "Chirag" to finish the same task, where "Chirag" is 20% less efficient than "Arjun." On the first day, "Arjun" began the work alone. On the second day, "Bhuvan" joined him, and on the third day, "Chirag" also joined, with all three continuing together for 12 days. Afterward, all three left the task, and the remaining work was finished by "Dinesh," who has an efficiency of 'd' units/day, in 8 days. The total work amounts to 300 units. Which of the following statements is/are true according to the information given above? I. 7.5d + 120 = 150 II. ‘Amit’ is 275% more efficient than ‘Dinesh’ III. ‘Bhuvan’ takes (3d + 28) days to complete the work alone.Solution
ATQ, Time taken by ‘Amit’ to complete the work = 20 days Therefore, time taken by ‘Chirag’ to complete the work = 20/0.8 = 25 days Time taken by ‘Bhuvan’ to complete the work = 25 + 5 = 30 days Let the total work = 300 units Efficiency of ‘Amit’ = 300/20 = 15 units/day Efficiency of ‘Bhuvan’ = 300/30 = 10 units/day Efficiency of ‘Chirag’ = 300/25 = 12 units/day Work done in 3 days = (15 + 15 + 10 + 15 + 12) = 67 units Work done in 12 days = 67 × 4 = 268 units Therefore, efficiency of ‘Dinesh’ = (300 – 268)/8 = 4 units/day Therefore, d = 4 Statement I: 7.5d + 120 = 30 + 120 = 150 Therefore, statement I is true Statement II: Efficiency of ‘Amit’ = 15 units/day Efficiency of ‘Dinesh’ = 4 units/day Required % = {(15 – 4)/4} × 100 = 275% Therefore, statement II is true. Statement III: Time taken by ‘Bhuvan’ to complete the work alone = 30 days 3d + 28 = 12 + 28 = 40 days Therefore, statement III is incorrect
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