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 hrs
(b) 20 hrs
(c) 18 hrs
(d) 15 hrs
The correct answers to the above question in:
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
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Read more basic pipes and cisterns problems Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
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 : 3
Pipe A can fill an empty tank in 6 hours and pipe B in 8 hours. If both the pipes are opened and after 2 hours pipe. A is closed, how much time B will take to fill the remaining tank?
a) 3$1/3$ hours
b) 7$1/2$ hours
c) 2$2/5$ hours
d) 2$1/3$ hours
Answer »Answer: (a)
Using Rule 1,
Part of tank filled by pipes A and B in 2 hours
= $2(1/6 + 1/8)$
=$2({4 + 3}/24) = 7/12$
Remaining part = $1 - 7/12 = 5/12$
This part is filled by pipe B.
Required time = $5/12$ × 8
= $10/3$ hours = 3$1/3$ hours
Question : 4
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 : 5
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 : 6
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
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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