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Q:

# A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 ${\color{Blue} m^{3}}$. The emptying capacity of the tank is 10 $\inline {\color{Blue} m^{3}}$ per minute heigher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?

 A) 50 m^3/min B) 60 m^3/min C) 72 m^3/min D) None of these

Answer:   A) 50 m^3/min

Explanation:

Let the filling capacity of the pump be x $\inline {\color{Black} m^{3}}$/min.

Then, emptying capacity of the pump=(x+10) $\inline {\color{Black} m^{3}}$/min.

so,$\inline {\color{Black} \frac{2400}{x}-\frac{2400}{x+10}=8\; \; \Leftrightarrow x^{2}+10x-3000=0}$

$\inline {\color{Black} \Leftrightarrow \left ( x-50 \right )+\left ( x+60 \right )=0\; \; \Leftrightarrow x=50}$

Q:

There is an empty reservoir whose capacity is 30 litres. There is an inlet pipe which fills at 5 L/min and there is an outlet pipe which empties at 4 L/min. Both the pipes function alternately for 1 minute. Assuming that the inlet pipe is the first one to function, how much time will it take for the reservoir to be filled up to its capacity?

 A) 49.5 min B) 50 min C) 51 min D) 52 min

Answer & Explanation Answer: C) 51 min

Explanation:

The work to be done = Capacity of reservoir  = 30 litres.

1st Minute $\inline \fn_jvn \small \Rightarrow$ inlet pipe opened $\inline \fn_jvn \small \Rightarrow$ 5 lit filled

2nd minute $\inline \fn_jvn \small \Rightarrow$ inlet pipe closed; outlet pipe opened $\inline \fn_jvn \small \Rightarrow$ 4 lit emptied

In 2 minutes (5 litres - 4 litres = 1lit) is filled into the reservoir.

It takes 2 minutes to fill 1lit $\inline \fn_jvn \small \Rightarrow$ it takes 50 minutes to fill 25 litres into the reservoir.

In the 51st minute inlet pipe is opened and the reservoir is filled.

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6 30
Q:

Three taps A,B and C can fill a tank in 12,15 and 20 hours respectively. If A is open all the time and B ,C are open for one hour each alternatively, the tank will be full in:

 A) 6 hrs B) 20/3 hrs C) 7 hrs D) 15/2 hrs

Answer & Explanation Answer: C) 7 hrs

Explanation:

$\inline {\color{Black} (A+B)'s\: 1\: hour\: work=\left ( \frac{1}{12}+\frac{1}{15} \right )=\frac{9}{60}=\frac{3}{20}}$$\inline {\color{Black} (A+C)'s\: 1\: hour\: work=\left ( \frac{1}{12}+\frac{1}{20} \right )=\frac{8}{60}=\frac{2}{15}}$  $\inline {\color{Black} Part \: \: filled \: in \: 2 \: hrs=\left ( \frac{3}{20} +\frac{2}{15}\right )=\frac{17}{60}}$

$\inline {\color{Black} Part \: \: filled \: in \: 6 \: hrs=(3\times \frac{17}{60})=\frac{17}{20}}$

$\inline {\color{Black} Remaining\; Part =\left ( 1-\frac{17}{20} \right )=\frac{3}{20}}$

Now, it is  the turn of A and B (3/20) part is filled by A and B in 1 hour.

therefore, Total  time taken to fill the tank =(6+1)hrs= 7 hrs

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10 845
Q:

12 buckets of water fill a tank when the capacity of each tank is 13.5 liters. How many buckets will be needed to fill the same tank,if the capacity of each bucket is 9 liters?

 A) 8 B) 15 C) 16 D) 18

Answer & Explanation Answer: D) 18

Explanation:

Capacity of the tank =(12 x 13.5) liters =162 liters.

Capacity of each bucket =9 liters

Number of buckets needed = 162/9 =18.

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4 1268
Q:

One pipe can fill a tank  three times as fast as another pipe. If together the two pipes can fill the tank in 36 min, then the slower alone will be able to fill the tank in:

 A) 81 min B) 108 min C) 144 min D) 192 min

Answer & Explanation Answer: C) 144 min

Explanation:

Let the slower pipe alone fill the tank in x minutes.

Then,faster pipe will fill it in x/3 minutes.

$\inline \fn_jvn {\color{Black}\therefore\; \; \frac{1}{x}+\frac{3}{x}=\frac{1}{36}\: \: \: \: \Leftrightarrow \: \: \: \frac{4}{x}=\frac{1}{36}\: \: \: \Leftrightarrow \: \: \: x=144\: min}$

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4 1047
Q:

A water tank is two-fifth full.Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes.If both the pipes are open,how long will it take to empty or fill the tank completely?

 A) 6 min.to empty B) 6 min.to fill C) 9 min.to empty D) 9 min.to fill

Answer & Explanation Answer: A) 6 min.to empty

Explanation:

Clearly,pipe B is faster than pipe A and so,the tank will be emptied.

part to be emptied = 2/5

part emptied by (A+B) in 1 minute=$\inline \fn_jvn {\color{Black}\left ( \frac{1}{6}-\frac{1}{10} \right )=\frac{1}{15}}$

$\inline \fn_jvn \Rightarrow \frac{1}{15}:\frac{2}{5}::1:x$

$\inline \fn_jvn \Rightarrow \frac{2}{5}\times 15=6mins$

so, the tank will be emptied in 6 min

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