Question 67

Working alone A can do the task in 27 hours and B can do it in 54 hours. Find C's share (in Rs) if A, B and C get paid Rs 4,320 for completing a task in 12 hours on which they worked together.

Solution

Let say, C completes the task in c hrs .

So, $$\frac{1}{27}+\frac{1}{54}+\frac{1}{c}=\frac{1}{12}\ .$$

or, $$\frac{1}{c}=\frac{1}{12}-\frac{1}{27}-\frac{1}{54}=\frac{27-12-6}{27\times12}=\frac{1}{36}\ .$$

So, c=36 .

A's share:B's share:C's share = $$\frac{1}{27}:\frac{1}{54}:\frac{1}{36}=4:2:3\ .$$

So, C will get = $$4320\times\frac{3}{9}=1440\ .$$

A is correct choice.

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