Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 3 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill ?

Correct Answer: 50 m^3/min

Explanation:

Let the filling capacity of the pump be x m 3/min. 

Then, emptying capacity of the pump=(x+10) m 3/min.  

so, 2400 x - 2400 x + 10 = 8 ? x 2 + 10 x - 3000 = 0 

 

? x - 50 + x + 60 = 0 ? x = 50

Correct Answer: 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= 1 6 - 1 10 = 1 15

 

1 15 : 2 5 : : 1 : x

 

2 5 * 15 = 6 m i n s

 

so, the tank will be emptied in 6 min

Correct Answer: 39

Correct Answer: 20 hrs

Explanation:

1/8 - 1/x = 1/10

 => x = 40 hrs

Correct Answer: 7 hrs

Explanation:

A + B ' s 1 h o u r w o r k = 1 12 + 1 15 = 9 60 = 3 20

A + C ' s 1 h o u r w o r k = 1 12 + 1 20 = 8 60 = 2 15  

 

p a r t f i l l e d i n 2 h r s = 3 20 + 2 15 = 17 60  

 

p a r t f i l l e d i n 6 h r s = 3 * 17 60 = 17 20  

 

  r e m a i n i n g p a r t = 1 - 17 20 = 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

Correct Answer: 120 gallons

Explanation:

Work done by the waste pipe in 1 minute = 1 15 - 1 20 + 1 24 = 1 15 - 11 120 = - 1 40 [-ve sign means emptying]

 

Volume of  1 40part = 3 gallons

 

Volume of whole = (3 x 40) gallons = 120 gallons.

Correct Answer: 51 min

Explanation:

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

 1^st Minute ---> inlet pipe opened ---> 5 lit filled

 2^nd minute ---> inlet pipe closed; outlet pipe opened ---> 4 lit emptied

 

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

It takes 2 minutes to fill 1lit ---> it takes 50 minutes to fill 25 litres into the reservoir.  

 

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

Correct Answer: 300 hrs

Explanation:

Volume of water collected in the tank in 1 hour

? (0.3 × 0.2 × 20km × 1000mts) = 1200 m cubic

If after t hours, the water is at height of 12m,

1200t=200×150×12 

? t = 300 Hours.

Correct Answer: 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.

Correct Answer: 144 min

Explanation:

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

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

= > 1 x + 3 x = 1 36 = > 4 x = 1 36 = > x = 144 m i n s