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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

A
B
C
D
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Text Explanation

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 10pm = 8x-7y   (1) .

Here A operates for 8 hours and B operates for 7 hours .

As per condition 2

We get Volume filled till 6pm = 4x-2y    (2)

Here A operates for 4 hours and B operates for 2 hours .

Now equating (1) and (2)

we get 8x-7y =4x-2y

so we get 4x =5y 

y =4x/5

So volume of tank = $8x - 7 \times \frac{4x}{5} = \frac{12x}{5}$

So time taken by A alone to fill the tank = $\frac{\frac{12x}{5}}{x}$= 12hrs 

= 144 minutes

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