CAT 2021 Question Paper | Quant Slot 2

CAT Previous Year Paper | CAT Quant Questions | Question 21

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 21 : Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then the tank becomes full at 6 pm. If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is

  1. 140
  2. 120
  3. 144
  4. 264

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Explanatory Answer

Let the filling rate of pipe A be ‘a’ and the rate of emptying the tank of pipe B be ‘b’.
Then from the given information we can say that, when pipe A is kept open from 2PM to 10PM, i.e. for 8 hours and pipe B drains from 3PM till 10PM (7 hours), the tank gets filled up.
8a - 7b = 1 [1]
Also, from the second statement,
A is kept open from 2 PM to 6 PM (4 hours), and B is kept open for 2 hours (4 PM to 6PM), the tank gets filled up.
4a - 2b = 1 [2]
Multiplying equation [2] and subtracting [1] from it we get
8a - 4b - (8a - 7b) = 2 - 1
7b - 4b = 1
b = 1/3
From here we can compute the value of a
Putting the value of b in eq [2]
4a - 2(1/3) = 1
4a - 2/3 = 1
4a = 1 + 2/3
4a = 5/3
a = 5/12
Hence the rate of filling is 5/12.
If only pipe a is kept open, the tank will get filled in, say ‘n’ hours
n a = 1
n (5/12) = 1
So, n = 12/5
= 2.4 hours
= 144 minutes

The answer is '144'

Choice C is the correct answer.

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