A pipe can fill a bucket in P hours and another can empty in Q hours.

1.	A pipe can fill a bucket in P hours and another can empty in Q hours. They can together fill it in (Q > P)1. \(\frac{{{\rm{PQ}}}}{{{\rm{Q}} - {\rm{P}}}}\) hours2. P – Q hours3. Q – P hours4. \(\frac{{{\rm{PQ}}}}{{{\rm{P}} - {\rm{Q}}}}\) hours
Answer» Correct Answer - Option 1 : \(\frac{{{\rm{PQ}}}}{{{\rm{Q}} - {\rm{P}}}}\) hours Given: A pipe can fill a bucket in P hours and another can empty in Q hours. Concept: If a tap can fill a tank in x hours, then the tank filled by the tap in 1 hour = 1/x of the total tank. Calculation: When both pipe are opened simultaneously, part of the bucket filled in 1 hours ⇒ \(\frac{1}{{\rm{P}}} - \frac{1}{{\rm{Q}}}{\rm{}} = {\rm{}}\frac{{{\rm{Q}} - {\rm{P}}}}{{{\rm{PQ}}}}\) ∴ Required time is \(\frac{{{\bf{PQ}}}}{{{\bf{Q}} - {\bf{P}}}}\) hours.

A pipe can fill a bucket in P hours and another can empty in Q hours. They can together fill it in (Q > P)1. \(\frac{{{\rm{PQ}}}}{{{\rm{Q}} - {\rm{P}}}}\) hours2. P – Q hours3. Q – P hours4. \(\frac{{{\rm{PQ}}}}{{{\rm{P}} - {\rm{Q}}}}\) hours

Answer» Correct Answer - Option 1 : \(\frac{{{\rm{PQ}}}}{{{\rm{Q}} - {\rm{P}}}}\) hours

Given:

A pipe can fill a bucket in P hours and another can empty in Q hours.

Concept:

If a tap can fill a tank in x hours, then the tank filled by the tap in 1 hour = 1/x of the total tank.

Calculation:

When both pipe are opened simultaneously, part of the bucket filled in 1 hours

⇒ \(\frac{1}{{\rm{P}}} - \frac{1}{{\rm{Q}}}{\rm{}} = {\rm{}}\frac{{{\rm{Q}} - {\rm{P}}}}{{{\rm{PQ}}}}\)

∴ Required time is \(\frac{{{\bf{PQ}}}}{{{\bf{Q}} - {\bf{P}}}}\) hours.

Discussion

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