CAT Quantitative Aptitude Questions | CAT Time and Work questions

The question is from Pipes and Cisterns: Pipe flow rate. Flow rates of A and B together and of A is given and we need to find out the flow rate of B. Note: Sum of the rate of flow of individual pipes gives the combined flow rate. 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.

Question 11: Pipe A can fill a tank in 12 hours. When it works along with Pipe B, it can fill the tank in 8 hours. In how many hours can pipe B fill the same tank independently?

1. 8 hrs
2. 12 hrs
3. 24 hrs
4. 16 hrs

Explanatory Answer

Method of solving this CAT Question from Pipes Cisterns and Work Time: Sum of the rate of flow of individual pipes gives the combined flow rate

Let the capacity of the tank be C.
Rate of Pipe A = \\frac{C}{A}\\)
Rate of Pipe B = \\frac{C}{B}\\)
Rate of Pipe A and Pipe B together = \\frac{C}{A}\\) + \\frac{C}{B}\\) = \\frac{C}{8}\\)
\\frac{C}{12}\\) + \\frac{C}{B}\\) = \\frac{C}{8}\\)
\\frac{C}{B}\\) = \\frac{C}{8}\\) - \\frac{C}{12}\\) = \\frac{C}{24}\\)
Pipe B independently will take 24 hours to fill the tank.

The question is "In how many hours can pipe B fill the same tank independently?"

Hence, the answer is "24 hrs".

Choice C is the correct answer.