Model 3 Opening both taps and leaks 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) r = p - q
(b) r = p + q
(c) $1/r = 1/p + 1/q$
(d) $1/r = 1/p - 1/q$
The correct answers to the above question in:
Answer: (d)
Since, P < q,
On opening pipe and sink together,
Part of the tub filled in 1 hour
= $1/P - 1/q$
Clearly, $1/P - 1/q = 1/r$
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Read more opening both taps and leaks Based Quantitative Aptitude Questions and Answers
Question : 1
A tank can be filled by two pipes in 20 minutes and 30 minutes respectively. When the tank was empty, the two pipes were opened. After some time, the first pipe was stopped and the tank was filled in 18 minutes. After how much time of the start was the first pipe stopped?
a) 12 minutes
b) 10 minutes
c) 5 minutes
d) 8 minutes
Answer »Answer: (d)
Let the first pipe be closed after x minutes
$x/20 + 18/30$ = 1
$x/20 = 1 - 18/30 = 1 - 3/5 = 2/5$
$x = 2/5 × 20$ = 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
Here, x = 20, y = 30, t = 18
Required time = $[x(1 –{t/y})]$
[Since, first pipe is closed]
= $[20(1 - 18/30)] = 20 × 12/30$ = 8 minutes
Question : 2
Two pipes A and B can fill a tank in 6 hours and 8 hours respectively. If both the pipes are opened together, then after how many hours should B be closed so that the tank is full in 4 hours?
a) $8/3$ hrs
b) 2 hrs
c) $2/3$ hrs
d) 1hrs
Answer »Answer: (a)
Part of the tank filled in 4 hours by pipe A = $4/6 = 2/3$
Remaining part = ${1 - 2}/3 = 1/3$
Time taken by pipe B in filling $1/3$ part = $8/3$ hours
Using Rule 8,
Here, x = 6, y = 8, t = 4
Required time = $[y(1 –{t/x})]$ hours
= $[8(1 - 4/6)]$ hours = $8/3$ hours
Question : 3
A tank can be filled with water by two pipes A and B together in 36 minutes. If the pipe B was stopped after 30 minutes, the tank is filled in 40 minutes. The pipe B can alone fill the tank in
a) 90 minutes
b) 75 minutes
c) 45 minutes
d) 60 minutes
Answer »Answer: (a)
Let the pipe B fill the tank in x minutes.
Part of the tank filled by pipes A and B in 1 minute = $1/36$
Part of the tank filled by pipe A in 1 minute
= $1/36 - 1/x$
According to the question,
30 × $1/x + 40(1/36 - 1/x) = 1$
$30/x + 10/9 - 40/x$ = 1
$40/x - 30/x = 10/9 - 1$
$10/x = 1/9 ⇒ x = 90$ minutes
Question : 4
Two pipes, P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes, P is turned off. In how many more minutes will Q fill the cistern ?
a) 8$1/4$ minutes
b) 8 minutes
c) 7 minutes
d) 7$1/2$ minutes
Answer »Answer: (a)
Using Rule 1,Two taps 'A' and 'B' can fill a tank in 'x' hours and 'y' hours respectively. If both the taps are opened together, then how much time it will take to fill the tank?Required time = $({xy}/{x + y})$ hrs
Part of the tank filled in 3 minutes by pipes P and Q
= $3(1/12 + 1/15)$
= $3({5 + 4}/60) = {3 × 9}/60 = 9/20$
So, Remaining part
= 1– $9/20 = 11/20$
Time taken by Q
= $11/20 × 15 = 33/4 = 8{1}/4$ 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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