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1. 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:

A. $\frac{2}{3}$ hours

B. $\frac{3}{4}$ hours

C. $\frac{3}{2}$ hours

D. $\frac{4}{3}$ hours

Solution:

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 (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.

\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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