A swimming pool can be filled by tap P and tap Q together in 36 minute

1.	A swimming pool can be filled by tap P and tap Q together in 36 minutes. If tap Q started first and stopped after 30 minutes, then the swimming pool is filled by a tap P in 40 minutes. In how much time the tap Q can fill the swimming pool alone?1. 45 minutes2. 60 minutes3. 75 minutes4. 90 minutes
Answer» Correct Answer - Option 4 : 90 minutes Given: A swimming pool can be filled by tap P and tap Q together in 36 minutes P open for 40 minutes and Q open for 30 minutes 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: Let the tap Q fill the tank in ‘a’ minutes. Part of the swimming pool filled by tap P in 1 minute = \(\frac{1}{{36}} - \frac{1}{{\rm{a}}}\) According to the question, ⇒ \({\rm{\;}}30 \times \frac{1}{{\rm{a}}}{\rm{}} + {\rm{}}40{\rm{}}\left( {\frac{1}{{36}} - \frac{1}{{\rm{a}}}} \right){\rm{\;}} = {\rm{}}1\) ⇒ \(\frac{{30}}{{\rm{a}}}{\rm{}} + {\rm{}}\frac{{10}}{9} - \frac{{40}}{{\rm{a}}}{\rm{}} = {\rm{}}1\) ⇒ \(\frac{{40}}{{\rm{a}}} - \frac{{30}}{{\rm{a}}}{\rm{}} = {\rm{}}\frac{{10}}{9} - 1\) ⇒ \(\frac{{10}}{{\rm{a}}}{\rm{}} = {\rm{}}\frac{1}{9}\) ⇒ a = 90 minutes ∴ Tap Q can fill the tank in 90 minutes.

A swimming pool can be filled by tap P and tap Q together in 36 minutes. If tap Q started first and stopped after 30 minutes, then the swimming pool is filled by a tap P in 40 minutes. In how much time the tap Q can fill the swimming pool alone?1. 45 minutes2. 60 minutes3. 75 minutes4. 90 minutes

Answer» Correct Answer - Option 4 : 90 minutes

Given:

A swimming pool can be filled by tap P and tap Q together in 36 minutes

P open for 40 minutes and Q open for 30 minutes

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:

Let the tap Q fill the tank in ‘a’ minutes.

Part of the swimming pool filled by tap P in 1 minute = \(\frac{1}{{36}} - \frac{1}{{\rm{a}}}\)

According to the question,

⇒ \({\rm{\;}}30 \times \frac{1}{{\rm{a}}}{\rm{}} + {\rm{}}40{\rm{}}\left( {\frac{1}{{36}} - \frac{1}{{\rm{a}}}} \right){\rm{\;}} = {\rm{}}1\)

⇒ \(\frac{{30}}{{\rm{a}}}{\rm{}} + {\rm{}}\frac{{10}}{9} - \frac{{40}}{{\rm{a}}}{\rm{}} = {\rm{}}1\)

⇒ \(\frac{{40}}{{\rm{a}}} - \frac{{30}}{{\rm{a}}}{\rm{}} = {\rm{}}\frac{{10}}{9} - 1\)

⇒ \(\frac{{10}}{{\rm{a}}}{\rm{}} = {\rm{}}\frac{1}{9}\)

⇒ a = 90 minutes

∴ Tap Q can fill the tank in 90 minutes.