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A and B complete a work in 17 days. If A alone can do it in 34 days then, B alone can do in______________(days).
33
35
34
36
34
Use the product/difference rule: if A and B together take x days and A takes y days, B takes yтИТxx├ЧyтАЛ days. Here, 34тИТ1717├Ч34тАЛ=1717├Ч34тАЛ=34.
Work completion by (A + B) = 17 days, Work completion by A alone = 34 days.
B1тАЛ=(A+B)1тАЛтИТA1тАЛ
Use the product/difference rule: if A and B together take x days and A takes y days, B takes yтИТxx├ЧyтАЛ days. Here, 34тИТ1717├Ч34тАЛ=1717├Ч34тАЛ=34.
Students often wrongly subtract the days directly (34тИТ17=17) or assume A and B must take different times; here, A works twice as fast as B, hence they share the load equally.
Define Rates
The rate of work of A and B together is 1/17 per day, and the rate of A is 1/34 per day.
RateA+BтАЛ=171тАЛ,RateAтАЛ=341тАЛ
Calculate B's rate
Subtract A's rate from the combined rate to find B's daily work rate.
RateBтАЛ=171тАЛтИТ341тАЛ=342тИТ1тАЛ=341тАЛ
Determine Days
Since B completes 1/34 of the work in one day, B takes 34 days to finish.
TimeBтАЛ=34┬аdays
C is correct because the calculation 1/17тИТ1/34 results in 1/34, meaning B requires 34 days to complete the work alone.
This concept is identical to the 'Pipe and Cistern' topic where inlet/outlet rates replace work rates.
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