Pipes and Cisterns Problems and Solutions

• 15. An electric pump can fill a tank in 3 hours. Because of a leak in the tank, it took 3 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty ?

  1. 10 hours
  2. 13 hours
  3. 17 hours
  4. 21 hours

  Answer :

  Option D

  Explanation:

  We can get the answer by subtrating work done by leak in one hour by subtraction of filling for 1 hour without leak and with leak, as
  
  Work done for 1 hour without leak = 1/3
  Work done with leak =
  \begin{aligned}
  3\frac{1}{2} = \frac{7}{2} \\
  \text{Work done with leak in 1 hr= }\frac{2}{7} \\
  \text{Work done by leak in 1 hr }\\
  = \frac{1}{3} - \frac{2}{7} = \frac{1}{21}
  \end{aligned}
  
  So tank will be empty by the leak in 21 hours.

• 16. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in

  1. 144 mins
  2. 140 mins
  3. 136 mins
  4. 132 minw

  Answer :

  Option A

  Explanation:

  Let the slower pipe alone fill the tank in x minutes
  then faster will fill in x/3 minutes.
  
  Part filled by slower pipe in 1 minute = 1/x
  Part filled by faster pipe in 1 minute = 3/x
  
  Part filled by both in 1 minute = \begin{aligned}
  \frac{1}{x} + \frac{3}{x}= \frac{1}{36} \\
  => \frac{4}{x} = \frac{1}{36} \\
  x = 36*4 = 144 mins
  \end{aligned}