Question 57

X alone can do a piece of work in 15 days. Y alone can do the same work in 30 days. X, Y and Z, working together, can complete the work in nine days. In how many days Z alone can complete the same work?

Solution

Let No. of days taken by X to complete the work i.e x = 15 days

No. of days taken by X to complete the work i.e y= 30 days

and z be the number of days taken by Z to complete the work

A/c to question ,

$$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} =\frac{1}{9}$$

$$\frac{1}{z} = \frac{1}{9} - \frac{1}{15} - \frac{1}{30}$$ = $$\frac{1}{90}$$

So, the answer would be option a)90.

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