a) $$\frac{2}{3}$$ hours
b) $$\frac{3}{4}$$ hours
c) $$\frac{3}{2}$$ hours
d) $$\frac{4}{3}$$ hours
Answer: d
Explanation: 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.
$$ \frac{1}{x} + \frac{1}{{x – 5}} + \frac{1}{{2\left( {x – 6} \right)}} = \frac{1}{{x – 6}}$$
On solving above equation, 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
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