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If A, B and C alone can complete a work in x, y and z days respectively, then in how many days will they complete the same work, working together?1. \(\frac{{x + y + z}}{{xyz}}\) days2. \(\frac{{xy + yz + zx}}{{xyz}}\) days3. \(\frac{{xyz}}{{xy + yz + zx}}\) days4. None of the above |
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Answer» Correct Answer - Option 3 : \(\frac{{xyz}}{{xy + yz + zx}}\) days Calculation A can complete work in 'x' days B can complete work in 'y' days C can complete work in 'z' days A's one-day work = 1/x B's one-day work = 1/y C's one-day work = 1/z A, B and C's one-day work = 1/x + 1/y + 1/z \(\Rightarrow {xy + yz + zx \over xyz}\) Time taken by A, B and C together to complete the work = 1/A, B and C's one-day work \(\Rightarrow \frac{{xyz}}{{xy + yz + zx}} days\) |
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