CAT Quantitative Aptitude Questions | CAT Time and Work questions

The question is from Pipes and Cisterns. Three pipes and the time taken to fill the tank by them is given and we need to find out "t". If you had three pipes and wanted to keep them open for different stretches of time, no one can stop you from doing that. Mathematicians are creatures of habit.

Question 2: Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. How long will it take C alone to fill the tank ?

1. 18
2. 36
3. 27
4. 24

Explanatory Answer

Method of solving this CAT Question from Pipes Cisterns and Work Time: If you had three pipes and wanted to keep them open for different stretches of time, no one can stop you from doing that.

A is kept open for all t minutes and fills one-third the tank. Or, A should be able to fill the entire tank in '3t' minutes.
A and B together can fill the tank completely in t minutes. A alone can fill it in 3t minutes.
A and B together can fill \\frac{1}{t}\\) of the tank in a minute. A alone can fill \\frac{1}{3t}\\) of the tank in a minute. So, in a minute, B can fill \\frac{1}{t}\\) - \\frac{1}{3t}\\) = \\frac{2}{3t}\\). Or, B takes \\frac{3t}{2}\\) minutes to fill an entire tank.
To fill one-third the tank, B will take \\frac{t}{2}\\) minutes. B is kept open for 10 minutes.
\\frac{t}{2}\\) = t - 10, t = 20 minutes.
A takes 60 minutes to fill the entire tank, B takes 30 minutes to fill the entire tank. A is kept open for all 20 minutes. B is kept open for 10 minutes.
C, which is kept open for 8 minutes also fills one-third the tank. Or, C alone can fill the tank in 24 minutes.

The question is "Find the time taken by C to fill the tank?"

Hence, the answer is "24".

Choice D is the correct answer.