Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?

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: 25

Explanation:

The toys are different; The boxes are identical
If none of the boxes is to remain empty, then we can pack the toys in one of the following ways
a. 2,2,1
b. 3,1,1

Case a. Number of ways of achieving the first option 2?2?1

Two toys out of the 5 can be selected in 5 C 2 5 ways. Another 2 out of the remaining 3 can be selected in 3 C 2 ways and the last toy can be selected in  1 C 1  way.

However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2.

Therefore, total number of ways of achieving the 2?2?1 option is:

5 C 2 * 3 C 2 2 = 10 * 3 2 = 15 ways.

Case b. Number of ways of achieving the second option 3?1?1

Three toys out of the 5 can be selected in 5 C 3  ways. As the boxes are identical, the remaining two toys can go into the two identical looking boxes in only one way.
Therefore, total number of ways of getting the 3?1?1 option is 5 C 3=10 ways.

Total ways in which the 5 toys can be packed in 3 identical boxes
=number of ways of achieving Case a + number of ways of achieving Case b
=15 + 10 = 25 ways

Correct Answer: 6

Explanation:

We get this using the formula of circular permutations i.e., (4 - 1)! = 3! =6

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: 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

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