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

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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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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]"