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)