QUANT QUIZ on Pipes & Cistern

1.    Two pipes A
and 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?
      (1)
20 hours
                       (2) 30 hours
(3) 15 hours                       (4)
25 hours

2.    Two pipes
can fill a tank in 10hours and 12 hours respectively while a third, pipe
empties the full tank in 20 hours. If all the three pipes operate
simultaneously, in how much time will the tank be filled?
(1) 8 hrs 30 min                 (2)
7 hrs 30 min
(3) 8 
hrs 38 min                (4) 7 hrs 38 min

3.    If two pipes
function simultaneously, the reservoir will be filled in 12 hours. One
pipe fills the reservoir 10 hours faster than the other. How many hours does
it take the second pipe to fill the reservoir?
(1) 10
hours                       (2) 40 hours
(3) 30 hours                       (4) 20 hours

4.    Two pipes A,B can fill a tank in 24 min. and 32
min. respectively. If both the pipes are opened simultaneously, after how much
time B should be closed so that the tank is full in 18 min.?
(1) 8 min                            (2)
12 min
(3) 15 min                          (4) 20
min

5.    Two pipes A and B can fill a tank in 36 min. and 45
min. respectively. A water pipe C can empty the tank in 30 min. First A and B
are opened. After 7 min, C is also opened. In how much time, the tank is full?
(1) 39 min                          (2)
40 min
(3) 42 min                          (4) 38
min

6.    Two pipes
can fill a cistern in 14 hours and 16 hours respectively. The pipes
are
opened simultaneously and it is found that due to leakage in the bottom it
took 32 minutes more to fill the cistern. When the cistern is full, in what
time will the leak empty it?

(1) 112 min                        (2) 
115 min
(3) 120 min                        (4)
110 min

7.     An electric pump can fill a tank in 3 hours.
Because of a leak in , the tank it took 3(1/2) hours to fill the tank. If
the tank is full, how much time will the leak take

to empty it?
(1) 28
hours                       (2) 25 hours
(3) 21
hours                       (4)
20 hours

8.    A cistern has two taps which fill it in 12 minutes
and 15minutes respectively. There is also a waste pipe in the cistern. When all
the 3 are opened, the empty cistern is full in 20 minutes. How long will the
waste pipe take to empty the full cistern?
(1) 20min                           (2)
40 min
(3) 30 min                          (4) 10
min

9.    Three
pipes A, B and C can fill a tank in 6 hours. After working at it together for 2
hours, C is closed and A and B can fill the remaining part in 7 hours. The
number of hours taken by C alone to fill the tank is:
(1) 10                                 (2) 14
(3) 12                                 (4)
12

10.  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?
(1) 3 hours 15 min             (2)
3 hours 45 min
(3) 3 hours 40 min             (4)
3 hours 50 min
ANSWERS WITH EXPLANATIONS:
1.    (1)
Explanation
:
Part filled
by A in 1 hour = (1/36);
Part filled by B in 1 hour = (1/45);
Part filled by (A + B) In 1 hour =(1/36)+(1/45)=(9/180)=(1/20)
Hence, both the pipes together will fill the tank in 20 hours.

2.   
(2)
Explantion:
Net part
filled In 1 hour =(1/10)+(1/12)-(1/20)=(8/60)=(2/15).
The tank will be full in 15/2 hrs = 7 hrs 30 min.

3.   
(3)
Explanation:
let the
reservoir be filled by first pipe in x hours.
Then ,second pipe fill it in (x+10)hrs.
Therefore (1/x)+(1/x+10)=(1/12)
 (x+10+x)/(x(x+10))=(1/12).
x^2 –14x-120=0
(x-20)(x+6)=0
x=20 [neglecting the negative value of x]
so, the second pipe will take (20+10)hrs.
(i.e) 30 hours to fill the reservoir

4.   
(1)
Explantion:
let B be
closed after x min. then ,
Part filled by (A+B) in x min. +part filled by A in (18-x)min.=1
Therefore x*((1/24)+(1/32))+(18-x)*(1/24)=1
(7x/96) +
((18-x)/24)=1.
7x +4*(18-x)=96.
Hence, be must be closed after 8 min.

5.   
(1)
Explanation:
Part filled
in 7 min. = 7*((1/36)+(1/45))=(7/20).
Remaining part=(1-(7/20))=(13/20).
Net part filled in 1min. when A,B and C are opened=(1/36)+(1/45)-(1/30)=(1/60).
Now,(1/60) part is filled in one minute.
(13/20) part is filled in (60*(13/20))=39
minutes.

6.   
(1)
Explanation:
Work done
by the two pipes in 1 hour =(1/14)+(1/16)=(15/112).
Time taken by these pipes to fill the tank = (112/15)hrs = 7 hrs 28 min.
Due to leakage, time taken = 7 hrs 28 min + 32 min = 8 hrs
Work done by (two pipes + leak) in 1 hour = (1/8).
Work done by the leak m 1 hour =(15/112)-(1/8)=(1/112).
Leak will empty the full cistern in 112
hours.

7.   
(4)
Explanation:
 
work done
by the leak in 1 hour=(1/3)-(1/(7/2))=(1/3)-(2/7)=(1/21).
The leak will empty .the tank in 21 hours.

8.   
(4)
Explanation:
Work done
by the waste pipe in 1min
=(1/20)-(1/12)+(1/15) = -1/10 [negative sign means emptying]
therefore the waste pipe will empty the full cistern in 10min

9.   
(2)
Explanation: (A+B+C) – (A+B) can give you the
answer.
(A+B+C) =1/6 and (A+B+C) in 2hrs=2/6 and remaining part 1-2/6=2/3.
So (A+B) in 7 hrs is 2/ (3*7) =2/21.
1/6-2/21=1/14 so answer is 14.

10. 
(2)
Explanation:
A tap can fill a tank in 6 hours.
After half the tank is filled i.e. after 3 hrs.
three more similar taps are opened i.e.
no. of taps to fill remaining half tank = 4 taps
when 1 tap is used = (3 hrs/1 tap)
when 4 taps are used = (3 hrs/4 taps)=45min
total= 3hrs+45min