A completes 80% of a work in 20 days. Then B joins A and they complete the remaining work in 3 days. How long will B alone take to complete the whole work?
37 $\frac{1}{2}$ days
A completes 80% of the work in 20 days, so A's rate is \(\frac{80}{20} = 4\%\) of the work per day.
The remaining 20% of the work is completed by A and B together in 3 days, so their combined rate is \(\frac{20}{3}\%\) per day.
B's rate alone is \(\frac{20}{3} - 4 = \frac{20 - 12}{3} = \frac{8}{3}\%\) per day.
Time for B to complete the whole work alone is \(\dfrac{100}{8/3} = \dfrac{300}{8} = 37\tfrac{1}{2}\) days.
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