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 ‘Bittu’ and ‘Sittu’ to complete the whole task = 45/0.6 = 75 days Time taken by ‘Ankit’ to complete total task = 32/0.40 = 80 days Let total work = 1200 units (LCM of 75 and 80) Efficiency of ‘Ankit’ = 1200/80 = 15 units/day Efficiency of (Bittu + Sittu) = 1200/75 = 16 units/day Let the efficiency of ‘Bittu’ be ‘b’ units/day Efficiency of ‘Sittu’ = 2.20 × b = 2.2b units/day According to the question, 2.2b + b = 16 Or, 3.2b = 16 Or, b = 5 Therefore, efficiency of ‘Bittu’ = b = 5 units/day Efficiency of ‘Sittu’ = 16 – 5 = 11 units/day Time taken by ‘Sittu’ to complete 22% of the task = (0.22 × 1200)/11 = 24 days
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