CAT Quantitative Aptitude Questions | CAT Time and Work questions

The question is from Time and work: Fetching water. Filling a tank manually, how hard can it be? 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 20: Bibhor takes 3 hours to fetch as much water as Ahmed can fetch in 2 hours. Deepak takes 5 hours to fetch as much water as Bibhor can fetch in 4 hours. A tank takes 20 hours to fill if all work together. What time would Bibhor take to fill the tank alone?

1. 50 hrs
2. 56 hrs
3. 77 hrs
4. 66 hrs

Explanatory Answer

Method of solving this CAT Question from Pipes Cisterns and Work Time: A small assumption would do the job!

Let the work done by Ahmed be 60 (LCM of 2,3,4,5)
So, work done per hour by:
Ahmed – \\frac{60}{2}\\) = 30
Bibhor – \\frac{60}{3}\\) = 20
Bibhor in 4 hours – 20 x 4 = 80
Deepak – \\frac{80}{5}\\) = 16
Therefore, total work done in an hour = 30 + 20 + 16 = 66
If all 3 work for 20 hours, total work done = 66 * 20
If Bibhor alone has to work, time taken to do 66 * 20 of work = 66 * \\frac{20}{20}\\) (work done by Bibhor in 1 hour)
= 66 hours

The question is "What time would Bibhor take to fill the tank alone?"

Hence, the answer is "66 hrs".

Choice D is the correct answer.