Aptitude- Pipes and Cistern

(11) Pipe A can fill a tank in 5 hours, and Pipe B can fill the same tank in 8 hours. If both pipes are opened simultaneously, how long will it take to fill half of the tank?

• (a) 2 hours and 40 minutes
• (b) 2 hours
• (c) 2 hours and 30 minutes
• (d) 1 hour and 30 minutes

Answer

Correct Answer: (b) 2 hours
Rate\ of\ A\ = \frac{1}{5}
Rate\ of\ B\ = \frac{1}{8}
Combined\ rate\ = \frac{1}{5} + \frac{1}{8} = \frac{13}{40}
Time\ taken\ to\ fill\ half\ of\ the\ tank\ = \frac{1}{2} \div \frac{13}{40} = \frac{20}{13} \approx 1.54\ hours
\approx 2\ hours

(12) Pipe A can fill a tank in 3 hours, and Pipe B can empty the same tank in 6 hours. If both pipes are opened simultaneously when the tank is empty, how long will it take to fill the tank?

• (a) 2 hours
• (b) 4 hours
• (c) 6 hours
• (d) 9 hours

Answer

Correct Answer: (d) 9 hours
Rate\ of\ A\ = \frac{1}{3}
Rate\ of\ B\ = -\frac{1}{6}
Combined\ rate\ = \frac{1}{3} - \frac{1}{6} = \frac{1}{2}
Time\ taken\ to\ fill\ the\ tank\ = \frac{1}{\frac{1}{2}} = 2\ hours
2\ hours\ to\ fill\ half\ of\ the\ tank
2\ hours\ to\ empty\ half\ of\ the\ tank
Total\ time\ to\ fill\ the\ tank\ = 2\ hours\ +\ 2\ hours\ =\ 4\ hours

(13) Pipe A can fill a tank in 7 hours, and Pipe B can empty the same tank in 10 hours. If both pipes are opened simultaneously when the tank is empty, how long will it take to fill the tank?

• (a) 5 hours
• (b) 6 hours
• (c) 14 hours
• (d) 35 hours

Answer

Correct Answer: (c) 14 hours
Rate\ of\ A\ = \frac{1}{7}
Rate\ of\ B\ = -\frac{1}{10}
Combined\ rate\ = \frac{1}{7} - \frac{1}{10} = \frac{3}{70}
Time\ taken\ to\ fill\ the\ tank\ = \frac{1}{\frac{3}{70}} = \frac{70}{3} \approx 23.33\ hours
\approx 24\ hours

(14) Pipe A can fill a tank in 9 hours, and Pipe B can empty the same tank in 12 hours. If both pipes are opened simultaneously when the tank is empty, how long will it take to fill the tank?

• (a) 6 hours
• (b) 8 hours
• (c) 18 hours
• (d) 36 hours

Answer

Correct Answer: (c) 18 hours
Rate\ of\ A\ = \frac{1}{9}
Rate\ of\ B\ = -\frac{1}{12}
Combined\ rate\ = \frac{1}{9} - \frac{1}{12} = \frac{1}{36}
Time\ taken\ to\ fill\ the\ tank\ = \frac{1}{\frac{1}{36}} = 36\ hours

(15) Pipe A can fill a tank in 15 hours, and Pipe B can fill the same tank in 10 hours. If both pipes are opened simultaneously, how long will it take to fill the tank?

• (a) 6 hours
• (b) 6 hours and 40 minutes
• (c) 7 hours
• (d) 8 hours

Answer

Correct Answer: (b) 6 hours and 40 minutes
Rate\ of\ A\ = \frac{1}{15}
Rate\ of\ B\ = \frac{1}{10}
Combined\ rate\ = \frac{1}{15} + \frac{1}{10} = \frac{1}{6}
Time\ taken\ to\ fill\ the\ tank\ = \frac{1}{\frac{1}{6}} = 6\ hours
= 6\ hours\ +\ \frac{2}{3}\ hour
= 6\ hours\ +\ 40\ minutes