Three men A. B and C working together can do a job in 6 hours less time than A alone, in 1 hour less time than B alone and in one half the time needed by C when working alone. Then A and B together can do the Job in

Let time taken by A alone = $$x$$ hours

=> Time taken by A, B & C together = $$(x-6)$$ hours

=> Time taken by B alone = $$(x-5)$$ hours

=> Time taken by C alone = $$2(x-6)$$ hours

Now, rate of work of A + rate of work of B + rate of work of C = rate of work of A,B,C together

=> $$\frac{1}{x} + \frac{1}{x-5} + \frac{1}{2(x-6)} = \frac{1}{x-6}$$

On solving above equation ,we get $$x = 3 , \frac{40}{6}$$

When $$x = 3$$ , the expression $$(x-6)$$ becomes negative, thus it's not possible.

=> $$x = \frac{40}{6}$$

Time taken by A & B together = $$\frac{1}{\frac{3}{20} + \frac{3}{5}}$$

= $$\frac{4}{3}$$ hours