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SIMPLE PROBLEMS
1)Two pipes A& B can fill a tank in 36 hours and 45 hours respectively. If
both the pipes are opened simultaneously, how much time will be taken to fill
the tank?
Sol: Part filled by A in 1 hour=1/36
Part filled by B in 1 hour= 1/45;
Part filled by (A+B)'s in 1 hour=1/36 +1/45= 9/180 =1/20
Hence, both the pipes together will fill the tank in 20 hours.
2)Two pipes can fill a tank in 10 hours & 12 hours respectively. While 3rd
pipe empties the full tank n 20 hours. If all the three pipes operate
simultaneously,in how much time will the tank be filled?
Sol: Net part filled in 1 hour=1/10 +1/12 -1/20
=8/60=2/15
The tank be filled in 15/2hours= 7 hrs 30 min
3)A cistern can be filled by a tap in 4 hours while it can be emptied by
another tap in 9 hours. If both the taps are opened simultaneously, then
after how much time will the cistern get filled?
Sol: Net part filled in 1 hour= 1/4 -1/9= 5/36
Therefore the cistern will be filled in 36/5 hours or 7.2 hours.
4)If two pipes function simultaneously, the reservoir will be filled in
12 days.One pipe fills the reservoir 10 hours faster than the other. How
many hours does it take the second pipe to fill the reservoir.
Sol: Let the reservoir be filled by the 1st pipe in x hours.
The second pipe will fill it in (x+10) hours
1/x + (1/(x+10))= 1/12
=> (2x+10)/((x)*(x+10))= 1/12
=> x=20
So, the second pipe will take 30 hours to fill the reservoir.
5)A cistern has two taps which fill it in 12 min and 15 min respectively.
There is also a waste pipe in the cistern. When all the three are opened,
the empty cistern is full in 20 min. How long will the waste pipe take to
empty the full cistern?
Sol: Work done by a waste pipe in 1 min=1/20 -(1/12+1/15)= -1/10 (-ve means emptying)
6)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?
Sol: Time taken by one tap to fill the half of the tank =3 hours
Part filled by the four taps in 1 hour=4/6=2/3
Remaining part=1 -1/2=1/2
Therefore, 2/3:1/2::1:x
or x=(1/2)*1*(3/2)=3/4 hours.
i.e 45 min
So, total time taken= 3hrs 45min.
7)A water tank is two-fifth full. Pipe A can fill a tank in 10 min. And B can
empty it in 6 min. If both pipes are open, how long will it take to empty or
fill the tank completely ?
Sol: Clearly, pipe B is faster than A and So, the tank will be emptied.
Part to be emptied=2/5.
Part emptied by (A+B) in 1 min= 1/6 -1/10=1/15
Therefore, 1/15:2/5::1:x or x=((2/5)*1*15)=6 min.
So, the tank be emptied in 6 min.
8)Bucket P has thrice the capacity as Bucket Q. It takes 60 turns for Bucket P
to fill the empty drum. How many turns it will take for both the buckets P&Q,
having each turn together to fill the empty drum?
Sol: Let the capacity of P be x lit.
Then capacity of Q=x/3 lit
Capacity of the drum=60x lit
Required number of turns= 60x/(x+(x/3))= 60x*3/4x=45
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