Aptitude- Pipes and Cistern

(1) A pipe can fill a tank in 4 hours, and a leak at the bottom can empty it in 8 hours. If both are opened simultaneously when the tank is empty, in how much time will the tank be filled?

• (a) 7 hours
• (b) 8 hours
• (c) 12 hours
• (d) 6 hours

Answer

Correct Answer: (b) 8 hours
Part\ filled\ by\ pipe\ in\ 1\ hour = \frac{1}{4}
Part\ emptied\ by\ leak\ in\ 1\ hour = -\frac{1}{8}
Net\ part\ filled\ in\ 1\ hour = \frac{1}{4} - (-\frac{1}{8}) = \frac{1}{4} + \frac{1}{8} = \frac{3}{8}
Time\ taken\ to\ fill\ the\ tank = \frac{1}{\frac{3}{8}} = \frac{8}{3} \approx 8\ hours

(2) Two pipes A and B can fill a cistern in 20 minutes and 30 minutes respectively. They are opened one after another with an interval of 5 minutes. How long will it take to fill the cistern?

• (a) 23 minutes
• (b) 25 minutes
• (c) 27 minutes
• (d) 28 minutes

Answer

Correct Answer: (c) 27 minutes
Part\ filled\ by\ A\ in\ 5\ minutes = \frac{5}{20} = \frac{1}{4}
Part\ remaining = 1 - \frac{1}{4} = \frac{3}{4}
Combined\ rate\ of\ A\ and\ B\ per\ minute = \frac{1}{20} + \frac{1}{30} = \frac{1}{12}
Time\ taken\ to\ fill\ \frac{3}{4}\ of\ the\ cistern = \frac{\frac{3}{4}}{\frac{1}{12}} = 9\ minutes
Total\ time = 5\ minutes\ +\ 9\ minutes = 27\ minutes

(3) Pipe A can fill a tank three times as fast as Pipe B. If together they can fill the tank in 36 minutes, how long will Pipe B alone take to fill the tank?

• (a) 144 minutes
• (b) 108 minutes
• (c) 96 minutes
• (d) 72 minutes

Answer

Correct Answer: (c) 96 minutes
Let\ the\ rate\ of\ B\ be\ \frac{1}{x}
then\ rate\ of\ A\ is\ \frac{3}{x}
Combined\ rate\ = \frac{1}{36}
\frac{3}{x} + \frac{1}{x} = \frac{1}{36}
\frac{4}{x} = \frac{1}{36},\ x = 144
so\ Pipe\ B\ alone\ will\ take\ 144\ minutes\ to\ fill\ the\ tank

(4) Pipe X can fill a tank in 6 hours, while Pipe Y can fill the same tank in 8 hours. If both pipes are opened simultaneously when the tank is empty, how long will it take to fill the tank?

• (a) 3 hours
• (b) 3.43 hours
• (c) 4 hours
• (d) 4.5 hours

Answer

Correct Answer: (b) 3.43 hours
Part\ filled\ by\ X\ in\ 1\ hour = \frac{1}{6}
Part\ filled\ by\ Y\ in\ 1\ hour = \frac{1}{8}
Net\ part\ filled\ in\ 1\ hour = \frac{1}{6} + \frac{1}{8} = \frac{7}{24}
Time\ taken\ to\ fill\ the\ tank = \frac{1}{\frac{7}{24}} = \frac{24}{7} \approx 3.43\ hours

(5) Pipe A can fill a cistern in 10 hours, and Pipe B can empty the same cistern in 20 hours. If both pipes are opened simultaneously when the cistern is empty, how long will it take to fill the cistern completely?

• (a) 15 hours
• (b) 10 hours
• (c) 30 hours
• (d) 40 hours

Answer

Correct Answer: (a) 15 hours
Part\ filled\ by\ A\ in\ 1\ hour = \frac{1}{10}
Part\ emptied\ by\ B\ in\ 1\ hour = -\frac{1}{20}
Net\ part\ filled\ in\ 1\ hour = \frac{1}{10} - (-\frac{1}{20}) = \frac{3}{20}
Time\ taken\ to\ fill\ the\ cistern = \frac{1}{\frac{3}{20}} = \frac{20}{3} = 15\ hours