Tips And Tricks And Shortcuts Of Pipes & Cisterns Questions

Type 2 : Tips and Tricks and Shortcuts for Pipes and Cisterns Problems related to Calculate time taken to fill a tank having a hole or leakage

Question 1. A pipe takes 5 hours to fill a water tank but because of leakage, it takes 3 hours more. Find out the number of hours taken by leakage pipe to empty the full water tank?

Options:

A. \frac{40}{3} hrs

B. \frac{3}{40} hrs

C. \frac{3}{47} hrs

D. \frac{2}{51} hrs

Solution:    Water tank filled in 5 hours = \frac{1}{5}

Now, due to outlet pipe, 1 hour part filled = \frac{1}{8}

Part of the water tank emptied in 1 hour = \frac{1}{5} – \frac{1}{8} = \frac{3}{40}

So, the leak will empty the full water tank in \frac{40}{3} hrs

Correct option: A

Type 3: Calculate Time Taken When Pipes Are Opened For Different Periods

Question 1: There are three pipes A, B and C, which can fill the tank in 10 hours. All the three pipes were opened for together for 5 hours, C is closed and inlets A and B fill the remaining part in 12 hours. Find the time taken by C alone to fill the tank.

Options:

A. 18 hrs 7 mins

B. 17 hrs 8 mins

C. 18 hrs

D. 17 hrs

Solution:     Part of the tank filled by the pipes A, B and C in 1 hour = \frac{1}{10}

Part of the tank filled by the pipes A, B and C in 5 hours = 5 * \frac{1}{10} = \frac{5}{10}= \frac{1}{2}

Remaining portion of tank to be filled = 1 – \frac{1}{2} = \frac{1}{2}

Now, when A and B are open

Part of the tank filled by A and B in 1 hour = \frac{ 1 x \frac{1}{2}}{ 12} = \frac{1}{24}

Therefore, part of the tank filled by C in 1 hour = \frac{1}{10}– \frac{1}{24} = \frac{7}{120}

Time taken by C alone = \frac{1}{ \frac{7}{120}} = \frac{120}{7} hours which can be written as 17 hrs 8 mins

Correct option: B