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CAT 2018 Question Paper | Quants Slot 2

CAT Previous Year Paper | CAT Pipes and Cisterns Questions | Question 27

If you go through the CAT Previous Year Paper, you'll notice that Pipes and Cisterns has a considerable presence in all of them and it would be prudent to have a good knowledge on this exciting topic. Not sure where to start? Start right here with this Pipes and Cistern question taken from CAT 2018 Question Paper.
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Question 27 : A water tank has inlets of two types A and B. All inlets of type A when open, bring in water at the same rate. All inlets of type B, when open, bring in water at the same rate. The empty tank is completely filled in 30 minutes if 10 inlets of type A and 45 inlets of type B are open, and in 1 hour if 8 inlets of type A and 18 inlets of type B are open. In how many minutes will the empty tank get completely filled if 7 inlets of type A and 27 inlets of type B are open? [TITA]

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Explanatory Answer

Method of solving this CAT Question from Pipes and Cisterns

Let A be the rate at which pipe A fills the tank in one minute and B be the rate at which pipe B fills in one minute
From the question, we can infer that 10A + 45B = $$frac{1}{30}$$Since it takes 30 minutes to fill, $$frac{1}{30}$th of the tank gets filled in 1 minute) Similarly, we can also infer that 8A + 18B = $\frac{1}{60}$ On simplifying, we get 2A + 9B = $\frac{1}{150}$ ---$1)
4A + 9B = $$frac{1}{120}$ ---$2)
Solving both, we get
2A = $$frac{1}{120}$ - $\frac{1}{150}$ A = $\frac{1}{1200}$ On substituting the value of A in the equation, we get B = $\frac{1}{1800}$ So, 7A + 27B = 7 × $\frac{1}{1200}$ + 27 × $\frac{1}{1800}$ = $\frac{7 + 18}{1200}$ = $\frac{1}{48}$ th of the tank in 1 minute So, the pipes fill the tank in 48 minutes The question is "A water tank has inlets of two types A and B. All inlets of type A when open, bring in water at the same rate. All inlets of type B, when open, bring in water at the same rate. The empty tank is completely filled in 30 minutes if 10 inlets of type A and 45 inlets of type B are open, and in 1 hour if 8 inlets of type A and 18 inlets of type B are open. In how many minutes will the empty tank get completely filled if 7 inlets of type A and 27 inlets of type B are open? [TITA]" Hence, the answer is 48 minutes Best CAT Online Coaching Try upto 40 hours for free Learn from the best! Prepare for CAT 2024 with 2IIM's Daily Preparation Schedule Know all about CAT Exam Syllabus and what to expect in CAT Already have an Account? CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar Best CAT Coaching in Chennai Attend a Demo Class Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! CAT Questions | CAT Quantitative Aptitude CAT Questions | Verbal Ability for CAT Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 How to reach 2IIM? Mobile:$91) 99626 48484 / 94459 38484
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