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# CAT 2018 Question Paper | Quants Slot 2

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

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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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##### 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 ###### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /- Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sat, Nov 2nd, 2019 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ##### 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? Phone:$91) 44 4505 8484
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