A and B can fill the tank in 60 min and 90 min. There is a leak at 3/4th of the height. If leak is opened alone, it takes 36 min to empty till 3/4th the height. Find the time taken to fill the tank if all of the taps and the leak are opened simultaneously.

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: 14

Explanation:

Part filled in 2 hours = 2/6=1/3

 

Remaining part = 1 - 1 3 = 2 3

 

 (A + B)'s 7 hour's work = 2/3

 

(A + B)'s 1 hour's work = 2/21

 

C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }

 

=1/6-2/21 = 1/14

 

C alone can fill the tank in 14 hours.

Correct Answer: 3 hrs 45 min

Explanation:

Time taken by one tap to fill half of the tank = 3 hrs.

 

  Part filled by the four taps in 1 hour =4*1/6 =2/3

 

Remaining part = 1 - 1 2 = 1 2

 

2 3 : 1 2 : : 1 : x

 

=> x =  1 2 * 1 * 3 2 = 3 4

 

So, total time taken = 3 hrs. 45 mins.

Correct Answer: 14 hours

Explanation:

If the total area of pump=1 part

The pumop take 2 hrs to fill 1 part 

The pumop take1 hour to fill 1/2 portion 

 

Due to lickage  

The pumop take 7/3 hrs to fill 1 part 

The pumop take1 hour to fill 3/7 portion 

Now the difference of area = (1/2-3/7)=1/14 

 

This 1/14 part of water drains in 1 hour 

Total area=1 part of water drains in (1x14/1)hours= 14 hours 

 

So the leak can drain all the water of the tank in 14 hours. 

Leak will empty the tank in 14 hrs

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: 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: 8.57 min

Explanation:

1/10 + 1/15 = 1/6 x 3 = 1/2

1 - 1/2 = 1/2

1/10 + 1/15 - 1/x = 1/2

x = 8.57 min

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.