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X alone can do a work in 10 days. Y alone can do the same in 15 days. X, Y and Z together can do the same work in 3 days. In how many days can Z alone do the work?
X alone can do a work in 10 days. Y alone can do the same in 15 days. X, Y and Z together can do the same work in 3 days. In how many days can Z alone do the work?
1). 6
2). 9
3). 4
4). 10
1 answers
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Let Z can do a work in z days.
⇒ Z will do 1/z amount of work in 1 day.
⇒ X and Y will do 1/10 and 1/15 amount of work in 1 day.
⇒ Total work done by all three in 1 day = 1/3
⇒ $(\frac{1}{{10}} + \frac{1}{{15}} + \frac{1}{z} = \frac{1}{3})$
⇒ $(\frac{1}{z} = \frac{1}{3} - \frac{1}{{10}} - \frac{1}{{15}} = \frac{{10 - 3 - 2}}{{30}} = \frac{5}{{30}} = \frac{1}{6})$
∴ Z will take 6 days to complete the work alone.