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Examoogle • User • info@examoogle.com • EE-2024-8821
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A এবং B যথাক্রমে 12 দিন এবং 18 দিনে একটি কাজ সম্পন্ন করতে পারে। যদি তারা একসাথে 6 দিন কাজ করে, তবে কাজের আর কত অংশ বাকি থাকবে?
91 অংশ কাজ
71 অংশ কাজ
21 অংশ কাজ
61 অংশ কাজ
61 অংশ কাজ
Calculate LCM of (12, 18) = 36 units. A's efficiency = 3, B's efficiency = 2. Combined = 5. In 6 days, they finish 5 × 6 = 30 units. Left = 36 - 30 = 6 units. Fraction left = 6/36 = 1/6.
Time taken by A = 12 days, Time taken by B = 18 days, Duration worked together = 6 days.
Work=TotaltimeTimeworked
Calculate LCM of (12, 18) = 36 units. A's efficiency = 3, B's efficiency = 2. Combined = 5. In 6 days, they finish 5 × 6 = 30 units. Left = 36 - 30 = 6 units. Fraction left = 6/36 = 1/6.
Many students calculate the work done (30/36 = 5/6) and mark it as the answer, forgetting the question asks for the work 'left to be done'.
Calculate Total Work
Assuming total work is the Least Common Multiple (LCM) of 12 and 18, which is 36 units.
Total Work=36units
Determine Individual Efficiencies
Efficiency is Work/Time. A's efficiency = 36/12 = 3 units/day. B's efficiency = 36/18 = 2 units/day.
(A+B)eff=3+2=5units/day
Calculate Work Completed
In 6 days of working together, total work completed is 6 days multiplied by combined efficiency.
Workdone=5×6=30units
Calculate Remaining Work
Subtract the completed work from total units and find the fraction of the job left.
Workleft=3636−30=366=61
D is correct because 30 out of 36 units of work were completed, leaving 6 units, which is 1/6 of the total job.
This LCM efficiency technique is identical to calculating the combined pipe fill rate in Pipe and Cistern problems.