CAT Quantitative Aptitude Questions | CAT Time and Work questions

The question is from Pipes and Cisterns: Pipe leakage. If there is a leakage in a pipe, how long will it take that pipe to drain the full tank? Mathematicians are creatures of habit. This topic has been called Pipes and Cisterns because someone named it like it long ago. Pipes and Tanks would be much better - at least makes it sound like wartime. Classic Pipes and Cisterns Question.

Question 15: A Two pipes can fill a tank in 12 hrs and 18 hrs respectively. The pipes are opened together but due to a pipe leakage , it takes 48 minutes extra to fill the tank, If the tank is full, what time will it take to completely empty due to the leakage.

1. 72 hrs
2. 84 hrs
3. 96 hrs
4. 112 hrs

Explanatory Answer

Method of solving this CAT Question from Pipes Cisterns and Work Time:

Time taken to fill the tank completely without leakage = \\frac{1}{(1/12) + (1/18)}\\) hrs
= \\frac{1}{(9 + 6)/108}\\) = \\frac{108}{15}\\) = 7 hours and 12 minutes
Given, it takes 48 minutes extra with the leakage. So, total time taken = 8 hours
= \\frac{1}{(1/12) + (1/18) - (1/x)}\\) = 8 (Where, x is the time taken by the leakage to completely empty the tank)
= \\frac{1}{12}\\) + \\frac{1}{18}\\) - \\frac{1}{8}\\) = \\frac{1}{x}\\)
= \\frac{(9 + 6 - 13.5)}{108}\\) = \\frac{1}{x}\\)
= x = \\frac{108}{1.5}\\) = 72 hours

The question is "what time will it take to completely empty due to the leakage."

Hence, the answer is "72 hrs".

Choice A is the correct answer.