Question 37

Work done by A in one day is four times the work done by B in one day, while the work done by B in one day is onethird of the work done by C in one day. C alone can complete the work in 16 days. In how many days can all the three together complete the work?

Solution

Let B's efficiency = $$x$$ units/day

=> A's efficiency = $$4x$$ units/day

and C's efficiency = $$3x$$ units/day

Time taken by C to complete the work alone = 16 days

=> Total work done = $$3x \times 16 = 48x$$ units

Sum of efficiencies of A, B and C = $$x + 4x + 3x = 8x$$ units/day

$$\therefore$$ Time taken by all to complete the work = $$\frac{48x}{8x}$$

= 6 days

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Work done by A in one day is four times the work done by B in one day, while the work done by B in one day is one­third of the work done by C in one day. C alone can complete the work in 16 days. In how many days can all the three together complete the work?