Question

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. \(\frac{{x + y + z}}{{xyz}}\) days
2. \(\frac{{xy + yz + zx}}{{xyz}}\) days
3. \(\frac{{xyz}}{{xy + yz + zx}}\) days
4. None of the above

Answer 1

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

\(\Rightarrow \frac{{xyz}}{{xy + yz + zx}} days\)