Question 69

Working together A, B and C can complete a task in 12 days. A and B can do the task in 55 days and 66 days respectively if they worked alone. In how many days can C do the task if he worked alone?

Solution

Let say, C alone take c days to complete the work .

So, $$\frac{1}{c}+\frac{1}{55}+\frac{1}{66}=\frac{1}{12}\ .$$

or, $$\frac{1}{c}=\frac{1}{12}-\frac{1}{55}-\frac{1}{66}=\frac{55-12-10}{660}=\frac{33}{660}=\frac{1}{20}\ .$$

or, $$c=20\ .$$

C is correct choice.

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