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) 7200 L
(b) 1200 L
(c) 2400 L
(d) 4500 L
The correct answers to the above question in:
Answer: (a)
Let the capacity of the tank = x litres
According to the question,
Quantity of water emptied by the leak in 1 hour = $x/10$ litres
Qunatity of water filled by the tap in 1 hour = 240 litres
According to the question,
$x/10 - x/15$ = 240
${3x - 2x}/30 = 240$
$x/30$ = 240
$x$ = 240 × 30 = 7200 litres
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Read more opening both taps and leaks Based Quantitative Aptitude Questions and Answers
Question : 1
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
Question : 2
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 : 3
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 : 4
Three pipes A, B and C can fill a tank in 6 hours. After working 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
a) 16
b) 14
c) 10
d) 12
Answer »Answer: (b)
A, B and C together fill the tank in 6 hours.
Part of the tank filled in 1 hour by (A + B + C) = $1/6$
Part of the tank filled in 2 hours by all three pipes
= $2/6 = 1/3$
Remaining empty part
= $1 - 1/3 = 2/3$
This $2/3$ part is filled by (A + B).
Time taken by (A + B) to fill the fully empty tank
= ${7 × 3}/2 = 21/2$ hours
Part of tank filled by C in 1 hour
= $1/6 - 2/21 = {7 - 4}/42 = 3/42 = 1/14$
∴ Required time = 14 hours.
Question : 5
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 ?
a) 3 hours 45 minutes
b) 3 hours 15 minutes
c) 4 hours
d) 4 hours 15 minutes
Answer »Answer: (a)
A tap can fill the tank in 6 hours. In filling the tank to its half, time required = 3 hours.
Remaining part = $1/2$
Since, 1 tap takes 6 hours to fill the tank
Time taken by 4 taps take to fill $1/2$ of the tank
= $6/4 × 1/2 = 3/4$ hour
Total time = $3 + 3/4$
= $3{3}/4$ hours = 3 hours 45 minutes
Question : 6
Three pipes A, B and C can fill a tank in 6 hours. After working together for 2 hours, C is closed and A and B fill the tank in 8 hours. The time (in hours) in which the tank can be filled by pipe C alone is
a) 9
b) 8
c) 10
d) 12
Answer »Answer: (d)
Part of the tank filled by
(A + B + C) in 1 hour = $1/6$
Part of tank filled by these in 2 hours
= $2/6 = 1/3$
Remaining part = $1 - 1/3 = 2/3$
Time taken by A and B in filling
$2/3$ rd part = 8 hours
Time taken by A and B in filling the whole tank
= ${8 × 3}/2$ = 12 hours
Part of tank filled by C in an hour
= $1/6 - 1/12 = 1/12$
Hence, required time = 12 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
pipes & cisterns Shortcuts and Techniques with Examples
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