Pipes and Cistern Questions

Q:

Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?

A) 10 min. 20 sec. B) 11 min. 45 sec.
C) 12 min. 30 sec. D) 14 min. 40 sec.
 
Answer & Explanation Answer: D) 14 min. 40 sec.

Explanation:

Part filled in 4 minutes ={\color{Black} 4\left ( \frac{1}{15}+\frac{1}{20} \right )=\frac{7}{15}}

Remaining part ={\color{Blue} \left ( 1-\frac{7}{15} \right )=\frac{8}{15}}

Part filled by B in 1 minute ={\color{Black} \frac{1}{20}}

{\color{Black}\therefore \frac{1}{20}:\frac{8}{15}::1:x}

{\color{Black}x=\left ( \frac{8}{15} \times 1\times 20\right )=10\frac{2}{3}min=10min.40sec.}

{\color{Black} \therefore }The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec

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Q:

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:

A) 10 B) 12
C) 14 D) 16
 
Answer & Explanation Answer: C) 14

Explanation:

Part filled in 2 hours ={\color{Black} \frac{2}{6}=\frac{1}{3}}

Remaining part ={\color{Black} \left ( 1-\frac{1}{3} \right )=\frac{2}{3}}

{\color{Black} \therefore } (A + B)'s 7 hour's work ={\color{Black} \frac{2}{3}}

(A + B)'s 1 hour's work ={\color{Black} \frac{2}{21}}

{\color{Black} }{\color{Black}\therefore }C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }

={\color{Black} \left ( \frac{1}{6}-\frac{2}{21} \right )=\frac{1}{14}}

{\color{Black} \therefore }C alone can fill the tank in 14 hours.

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Q:

A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 . The emptying capacity of the tank is 10 per minute heigher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?

A) 50 m^3/min B) 60 m^3/min
C) 72 m^3/min D) None of these
 
Answer & Explanation Answer: A) 50 m^3/min

Explanation:

Let the filling capacity of the pump be x /min.

Then, emptying capacity of the pump=(x+10) /min.

so,

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Q:

A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

A) 3 hrs 15 min B) 3 hrs 45 min
C) 4 hrs 15 min D) 4 hrs 1
 
Answer & Explanation Answer: B) 3 hrs 45 min

Explanation:

Time taken by one tap to fill half of the tank = 3 hrs.

Part filled by the four taps in 1 hour ={\color{Black} \left ( 4\times \frac{1}{6} \right )=\frac{2}{3}}

Remaining part ={\color{Black} \left ( 1- \frac{1}{2} \right )=\frac{1}{2}}

{\color{Black} \therefore \frac{2}{3}:\frac{1}{2} ::1:x}

{\color{Black} \Rightarrow x=\left ( \frac{1}{2} \times 1\times \frac{3}{2}\right )=\frac{3}{4}}

So, total time taken = 3 hrs. 45 mins.

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Q:

A pump can fill a tank with water in 2 hours. Because of a leak, it took  hours to fill the tank. The leak can drain all the water of the tank in:

A) 7 hours B) 8 hours
C) 12 hours D) 14 hours
 
Answer & Explanation Answer: D) 14 hours

Explanation:

Work done by the leak in 1 hour ={\color{Black} \left ( \frac{1}{2}-\frac{3}{7} \right )=\frac{1}{14}}

{\color{Black} \therefore } Leak will empty the tank in 14 hrs

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