Question
Ankit began a task but left it
after working for 32 days. The remaining 60% of the task was then completed by Bittu and Sittu working together over 45 days. Sittu is 120% more efficient than Bittu. Determine how long Sittu would take to complete 22% of the task on his own.Solution
ATQ, Total time taken by āBittuā and āSittuā to complete the whole task = 45/0.6 = 75 days Time taken by āAnkitā to complete total task = 32/0.40 = 80 days Let total work = 1200 units (LCM of 75 and 80) Efficiency of āAnkitā = 1200/80 = 15 units/day Efficiency of (Bittu + Sittu) = 1200/75 = 16 units/day Let the efficiency of āBittuā be ābā units/day Efficiency of āSittuā = 2.20 Ć b = 2.2b units/day According to the question, 2.2b + b = 16 Or, 3.2b = 16 Or, b = 5 Therefore, efficiency of āBittuā = b = 5 units/day Efficiency of āSittuā = 16 ā 5 = 11 units/day Time taken by āSittuā to complete 22% of the task = (0.22 Ć 1200)/11 = 24 days
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