CAT Exam 2021 Slot 2 Solved Paper

Question : 66 of 66

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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

Validate

Solution:

Let

\A

fill the tank at

x

liters/hour and

B

drain it at

y

liters/hour
Now as per Condition 1 :
We get Volume filled till

10 \pm = 8 x - 7 y

...(1)

Here A operates for 8 hours and B operates for 7 hours .
As per condition 2
We get Volume filled till 6pm =

4 x - 2y

...(2)

Here A operates for 4 hours and B operates for 2 hours .
Now equating (1) and (2)
we get

8 x - 7 y = 4 x - 2 y

so we get

4 x =5 y

y = {4 x}/5

So volume of tank =

8\x - 7 × {4 x }/5 = {12 x}/5

So time taken by A alone to fill the tank =

{12x}/5

x = 12/{5 \hrs}= 144 \minute

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