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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 19-times of the same work in ______________(days).
77
4
76
5
76
Use the product/difference rule: If A and B take x days and A takes y days, B takes yтИТxxyтАЛ days. For x=2 and y=4, B=4тИТ22├Ч4тАЛ=4 days.
A and B complete the work in 2 days. A alone completes it in 4 days. We need to find the time for B to complete 19 times the work.
B1тАЛ=A+B1тАЛтИТA1тАЛ
Use the product/difference rule: If A and B take x days and A takes y days, B takes yтИТxxyтАЛ days. For x=2 and y=4, B=4тИТ22├Ч4тАЛ=4 days.
Students often calculate the time for B to complete 1 unit of work (4 days) and forget to multiply by the factor of 19 requested in the question.
Calculate B's daily work efficiency
The combined efficiency of A and B is 1/2 of the work per day. A's efficiency is 1/4 of the work per day. B's efficiency is 1/2тИТ1/4=1/4 of the work per day.
EfficiencyBтАЛ=21тАЛтИТ41тАЛ=41тАЛ
Calculate time for B to finish 1 unit of work
Since B completes 1/4 of the work in 1 day, B takes 4 days to finish 1 full unit of work.
TimeBтАЛ=1/41тАЛ=4┬аdays
Calculate time for 19 times the work
To complete 19 times the work, multiply B's time for 1 unit by 19.
Total┬аTime=4├Ч19=76┬аdays
C is correct because B completes the work in 4 days, so 19 times the work requires 4 multiplied by 19, which equals 76 days.
This concept of work efficiency is directly applicable to pipe and cistern problems, where the same logic of adding/subtracting filling rates applies.
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