Question 69

C is 5 times as productive as B. A takes 60 days to complete a task. If A, B and C work together they can complete the task in 12 days. In how many days can B complete the task if he worked alone?

Solution

Let say, B can do in b days.

So, C can do in $$\left(\frac{b}{5}\ \right)$$ days.

So, in 1 day A,B,C will do = $$\left(\frac{1}{b}+\frac{5}{b}+\frac{1}{60}\right).$$

So, $$\left(\frac{1}{b}+\frac{5}{b}+\frac{1}{60}\right)=\frac{1}{12}\ .$$

or, $$\frac{6}{b}=\frac{1}{12}-\frac{1}{60}=\frac{5-1}{60}=\frac{4}{60}=\frac{1}{15}.$$

or, $$b=90\ .$$

So, C is correct choice.

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