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A is thrice as good a workman as B and therefore able to finish a piece of work in 60 days less than B. How much time will they both take to finish it together
Let time taken by B = $$t$$ days, and thus time taken by A = $$(t-60)$$ days
Since, efficiency is inversely proportional to time,
=> $$\frac{3}{1}=\frac{t}{t-60}$$
=> $$3t-180=t$$
=> $$2t=180$$
=> $$t=\frac{180}{2}=90$$
Thus, time taken by B is 90 days and by A is 30 days
=> Time taken by them to finish the work together = $$1\div(\frac{1}{90}+\frac{1}{30})$$
= $$\frac{90}{4}=22\frac{1}{2}$$ days
=> Ans - (B)
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