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Three men A, B, C working together can do a job in 6 hours less time than A alone, in one 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:

Correct Answer: $$\frac{4}{3}$$ hours
Time taken by A =x hours.Therefore taken by A, B and C together = (x - 6)Time taken by B = (x - 5)Time taken by C = 2(x - 6)Now, rate of work of A + Rate of work of B + Rate of work of C = Rate of work of ABC.$$ \Rightarrow \frac{1}{x} + \frac{1}{{x - 5}} + \frac{1}{{2\left( {x - 6} \right)}} = \frac{1}{{x - 6}}$$
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.
$$ \Rightarrow x = \frac{{40}}{6}$$
Time taken by A & B together = $$\frac{1}{{\frac{3}{{20}} + \frac{3}{5}}}$$
= $$\frac{4}{3}$$ hours

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