Model 1 Basic Pipes & Cisterns problems Practice Questions Answers Test with Solutions & More Shortcuts
pipes & cisterns PRACTICE TEST [3 - EXERCISES]
Model 1 Basic Pipes & Cisterns problems
Model 2 Filling tank by parts or fractions
Model 3 Opening both taps and leaks
Question : 11 [SSC CPO S.I.2005]
A tap can fill a cistern in 8 hours and another tap can empty it in 16 hours. If both the taps are open, the time (in hours) taken to fill the tank will be :
a) 24
b) 8
c) 10
d) 16
Answer »Answer: (d)
Part of the cistern filled in 1 hour = $1/8$
Part of the cistern emptied in 1 hour = $1/16$
When both the taps are opened simultaneously, part of cistern filled in 1 hour
= $1/8 - 1/16 = {2 - 1}/16 = 1/16$
Hence, the cistern will be filled in 16 hours.
Using Rule 7,
Here, x = 8, y = 16
Required time = ${xy}/{y- x}$
= ${8 × 16}/{16 - 8}$ = 16 hours
Question : 12 [SSC CHSL 2014]
Two pipes A and B can fill a tank in 36 minutes and 45 minutes respectively. Another pipe C can empty the tank in 30 minutes. First A and B are opened. After 7 minutes, C is also opened. The tank is filled up in
a) 45 minutes
b) 39 minutes
c) 46 minutes
d) 40 minutes
Answer »Answer: (c)
Part of the tank filled by pipes A and B in 1 minute
= $1/36 + 1/45 = {5 + 4}/180$
= $9/180 = 1/20$
Part of the tank filled by these pipes in 7 minutes
= $7/20$
Remaining unfilled part
= $1 - 7/20 = {20 - 7}/20 = 13/20$
When all three pipes are opened.
= $1/20 - 1/30 = {3 - 2}/60 = 1/60$
Time taken in filling $13/20$ part
= $13/20$ × 60 = 39 minutes
Required time = 39 + 7 = 46 minutes
Question : 13
Two pipes X and Y can fill a cistern in 24 minutes and 32 minutes respectively. If both the pipes are opened together, then after how much time (in minutes) should Y be closed so that the tank is full in 18 minutes ?
a) 5
b) 10
c) 8
d) 6
Answer »Answer: (c)
If pipe y be closed after x minutes, then
$18/24 + x/32$ = 1
$x/32 = 1 - 18/24 = 1- 3/4 = 1/4$
$x = 32/4$ = 8 minutes
Using Rule 8,Two taps A and B can fill a tank in x hours and y hours respectively. If both the pipes are opened together, then the time after which pipe B should be closed so that the tank is full in t hoursRequired time = $[y(1 –{t/x})]$ hours
x = 24, y = 32, t = 18
Required time = $[y(1 –{t/x})]$ minutes
= $[32(1 - {18/24})]$ minutes
= $[32(1 - {3/4})] = 32 × 1/4$ = 8 minutes
Question : 14 [SSC CGL Prelim 2004]
Two pipes can fill a cistern in 3 hours and 4 hours respectively and a waste pipe can empty it in 2 hours. If all the three pipes are kept open, then the cistern will be filled in :
a) 12 hours
b) 5 hours
c) 8 hours
d) 10 hours
Answer »Answer: (a)
Using Rule 2,
Part of the cistern filled in 1 hour
= $1/3 + 1/4 - 1/2$
[Cistern filled by 1st pipe + Cistern filled by 2nd pipe - Cistern emptied by 3rd pipe]
= ${4 + 3 - 6}/12 = 1/12$
Hence, the cistern will be filled in 12 hours.
Question : 15 [SSC CHSL 2013]
If two pipes function simultaneously, a tank is filled in 12 hours. One pipe fills the tank 10 hours faster than the other. How many hours does the faster pipe alone take to fill the tank?
a) 12 hrs
b) 20 hrs
c) 18 hrs
d) 15 hrs
Answer »Answer: (b)
Using Rule 1,
If the slower pipe fills the tank in x hours, then
$1/x + 1/{x - 10} = 1/12$
${x -10 + x}/{x(x - 10)} = 1/12$
$x^2 - 10x = 24x - 120$
$x^2 - 34x + 120$ = 0
$x^2 - 30x - 4x + 120$ = 0
$x (x - 30) - 4 (x - 30)$ = 0
$(x - 4) (x - 30)$ = 0
$x$ = 30 because $x ≠ 4$
Required time = 30 - 10 = 20 hours
IMPORTANT quantitative aptitude EXERCISES
Model 1 Basic Pipes & Cisterns problems Shortcuts »
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