A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

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: 14 min. 40 sec.

Explanation:

Part filled in 4 minutes =4(1/15+1/20) = 7/15

 

Remaining part =(1-7/15) = 8/15

 

Part filled by B in 1 minute =1/20 : 8/15 :: 1:x 

x = (8/15*1*20) =  10 2 3 m i n = 10 m i n 40 s e c

The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec

Correct Answer: 14! × 2

Explanation:

(16 ? 2)! × 2 = 14! × 2

Correct Answer: 3969

Explanation:

We can select atleast one item from 6 different items =  2 6 - 1  

 

Similarly we can select atleast one item from other set of 6 different items in  2 6 - 1 ways. 

 

Required number of ways =  ( 2 6 - 1 ) 2 6 - 1 = 2 6 - 1 2 = 3969

Correct Answer: 4096

Explanation:

Every ball can be distributed in 4 ways. 

Hence the required number of ways = 4 x 4 x 4 x 4 x 4 x 4 = 4096

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: 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: 20 hrs

Explanation:

1/8 - 1/x = 1/10

 => x = 40 hrs

Correct Answer: 39

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