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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 21-times of the same work in ______________(days).
4
84
5
85
4
Use the work efficiency formula: B=A−(A+B)A×(A+B). Here, B=4−24×2=4 days for one work; hence 21×4=84 days for 21-times the work.
Work done by (A + B) = 2 days, Work done by A alone = 4 days.
B1=(A+B)1−A1
Use the work efficiency formula: B=A−(A+B)A×(A+B). Here, B=4−24×2=4 days for one work; hence 21×4=84 days for 21-times the work.
Students often calculate the time for 1 work (4 days) and mark option A, forgetting the question asks for 21-times the work.
Calculate B's rate
Since (A+B) complete the work in 2 days and A takes 4 days, the rate of B is the difference: B1=21−41=41.
B1=41
Time for one work
If the rate of B is 41 of the work per day, B completes one work in 4 days.
B=4 days
Calculate for 21-times work
To complete 21-times the work, multiply the time taken for one work by 21: 21×4=84 days.
21×4=84 days
B is correct because calculating the time for one work as 4 days leads to 84 days for 21-times the work.
This concept of rates is identical to pipe-and-cistern problems where one pipe acts as an outlet (negative work).
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