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13 votes
13 votes

It takes $30$ minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets fully filled in $10$ minutes? 

  1. $4$ times the draining rate 
  2. $3$ times the draining rate
  3. $2.5$ times the draining rate
  4. $2$ times the draining rate
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6 Answers

Best answer
19 votes
19 votes

Let the capacity of tank be $1$ litre.

Draining rate $=\dfrac{0.5\text{ litre}}{30\text{ minutes}}=\dfrac{1}{60} \text{ litre/min}$

Let filling rate be $x \text{ litre/min}$

In $1$ min tank gets $x- \left(\dfrac{1}{60}\right) \text{litre}$ filled.

To fill the remaining half part we need $10 \text{ minutes}$

$x-\dfrac{1}{60} \text{ litre}\to 1 \text{ min}$

$0.5 \text{ litre}\to 10 \text{ mins}$

$\frac{0.5}{\left(x-\frac{1}{60}\right)}=10$

Solving, we get $x= \dfrac{4}{60}$ which is $4$ times more than draining rate.
So, option A

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5 votes
5 votes
Here is my approach:

A empty in the 30 minutes, so rate is 1 litre/minute (negative rate)

Now let B be a pump filling tank.

so now A+B work together and fill tank in 10 minutes , in that period B will drain some water i.e 10 minutes*1=10L

so net work , A-10=30

A=40 so ,A should work 4 times more as to fill the tank in 10 minutes.
1 votes
1 votes

A 444 times the draining rate 44444   444 times the draining rate444  times the draining rate erfgvguhn

Answer:

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