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A and B complete a work in 2 days. If A alone can do it in 4 days then, B alone can do 17-times of the same work in ______________(days).
4
68
5
69
68
Use the formula TBтАЛ=TAтАЛтИТTA+BтАЛTAтАЛ├ЧTA+BтАЛтАЛ. Here, TBтАЛ=4тИТ24├Ч2тАЛ=4 days. For 17 times the work, simply multiply the time by 17: 4├Ч17=68.
Time taken by A and B together (A+B) = 2 days. Time taken by A alone = 4 days. Target work = 17 times the original work.
Work=Efficiency├ЧTime
Use the formula TBтАЛ=TAтАЛтИТTA+BтАЛTAтАЛ├ЧTA+BтАЛтАЛ. Here, TBтАЛ=4тИТ24├Ч2тАЛ=4 days. For 17 times the work, simply multiply the time by 17: 4├Ч17=68.
Students often forget to multiply the individual time of B by the requested factor (17), answering '4' instead of '68'.
Calculate B's efficiency
Assuming total work is the LCM of 2 and 4, which is 4 units. Efficiency of (A+B) = 4/2=2 units/day. Efficiency of A = 4/4=1 unit/day.
EffBтАЛ=EffA+BтАЛтИТEffAтАЛ=2тИТ1=1┬аunit/day
Find B's time for one unit of work
Time taken by B to complete the work alone is 4┬аunits/1┬аunit/day=4 days.
TBтАЛ=14тАЛ=4┬аdays
Calculate time for 17-times the work
Since B takes 4 days to finish 1 work, to finish 17 works, B will take 4├Ч17 days.
17├Ч4=68┬аdays
B is correct because B finishes the work in 4 days, so 17 times that work requires 4 multiplied by 17, which equals 68 days.
This concept of 'Efficiency = Work / Time' is fundamental to Pipes and Cisterns problems as well. Always calculate efficiency first for complex group-work questions.
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