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
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) =
The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec
(16 ? 2)! × 2 = 14! × 2
We can select atleast one item from 6 different items =
Similarly we can select atleast one item from other set of 6 different items in ways.
Required number of ways = = 3969
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
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 ways. Another 2 out of the remaining 3 can be selected in
ways and the last toy can be selected in
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:
ways.
Case b. Number of ways of achieving the second option 3?1?1
Three toys out of the 5 can be selected in
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
=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
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 =
=> x =
So, total time taken = 3 hrs. 45 mins.
Part filled in 2 hours = 2/6=1/3
Remaining part =
(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.
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
1/8 - 1/x = 1/10
=> x = 40 hrs
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