Discussion
A alone would take 27 hours more to complete a work than A and B together. B takes 3 hours more to complete a work alone than A and B together. In how many days can A alone do it?
Answer: B
Let the time taken by A and B together be x hours. Then A takes x+27 hours and B takes x+3 hours. Their combined one hour's work is \(\frac{1}{x+27} + \frac{1}{x+3} = \frac{1}{x}\). This gives \(x(x+3+x+27) = (x+27)(x+3) \Rightarrow x(2x+30) = x^2+30x+81 \Rightarrow 2x^2+30x = x^2+30x+81 \Rightarrow x^2=81 \Rightarrow x=9\). Time taken by A alone = x+27 = 9+27 = 36 hours.
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