Model 1 Basic Pipes & Cisterns problems Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 3 EXERCISES
The following question based on pipes & cisterns topic of quantitative aptitude
(a) 12 hours
(b) 5 hours
(c) 8 hours
(d) 10 hours
The correct answers to the above question in:
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.
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Read more basic pipes and cisterns problems Based Quantitative Aptitude Questions and Answers
Question : 1
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
Question : 2
Three taps A, B, C can fill an overhead tank in 4, 6 and 12 hours respectively. How long would the three taps take to fill the tank if all of them are opened together ?
a) 5 hrs.
b) 2 hrs.
c) 4 hrs.
d) 3 hrs.
Answer »Answer: (b)
Using Rule 2,
Part of the tank filled by all three taps in an hour
= $1/4 + 1/6 + 1/12 = {6 + 4 + 2}/24 = 1 2$
Hence, the tank will be filled in 2 hours.
Question : 3
Two pipes A and B can separately fill a tank in 2 hours and 3 hours respectively. If both the pipes are opened simultaneously in the empty tank, then the tank will be filled in
a) 1 hour 20 minutes
b) 1 hour 12 minutes
c) 2 hours 30 minutes
d) 1 hour 15 minutes
Answer »Answer: (b)
Using Rule 1,
Part of tank filled by pipes A and B in 1 hour
= $1/2 + 1/3 = {3 + 2}/6 = 5/6$ parts
Required time = $6/5$ hours
= 1 hour $1/5$ × 60
= 1 hour 12 minutes
Question : 4
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 : 5
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 : 6
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
GET pipes & cisterns PRACTICE TEST EXERCISES
Model 1 Basic Pipes & Cisterns problems
Model 2 Filling tank by parts or fractions
Model 3 Opening both taps and leaks
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