Discussion
A is twice as good as workman as B and therefore able to finish a piece of work in 30 days less than B. In how many days can they complete the whole work; working together?
Answer: A
Working together they finish in 20 days.
A is twice as efficient as B, so B takes twice as long as A. If A takes \(x\) days, B takes \(2x\), and the difference is 30 days:
\[ \begin{aligned} 2x - x &= 30 \Rightarrow x = 30 \\ \text{A} &= 30 \text{ days}, \ \text{B} = 60 \text{ days} \end{aligned} \]
\[ \begin{aligned} \frac{1}{30} + \frac{1}{60} &= \frac{3}{60} \\ &= \frac{1}{20} \end{aligned} \]
So together they do one-twentieth of the work a day and need 20 days.
60 days is B's time working alone. 40 and 80 days are longer than A's own 30 days, which is impossible once B helps.
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