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) 120
(b) 108
(c) 72
(d) 84
The correct answers to the above question in:
Answer: (a)
Using Rule 7,
Tricky Approach
Part of the cistern filled in 1 minute by both the taps
= $1/40 - 1/60 = {3 - 2}/120 = 1/120$
Empty cistern will be filled in 120 minutes.
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Read more opening both taps and leaks Based Quantitative Aptitude Questions and Answers
Question : 1
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternatively, the tank will be full in :
a) 7$1/2$ hours
b) 7 hours
c) 6 hours
d) 6$1/2$ hours
Answer »Answer: (b)
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 filled by A and B in 1 hour
= $1/12 + 1/15 = {5 + 4}/60 = 3/20 +$...(i)
Part filled by A and C in the next 1 hour
= $1/12 + 1/20 = {5 + 3}/60 = 2/15$
Part filled in 2 hours
= $3/20 + 2/15 = {9 + 8}/60 = 17/20$
Part filled in 6 hours = $51/60$
Remaining part
= $1 - 51/60 = 9/60 = 3/20$
This part will be filled by (A+B) in 1 hour. [By (i)]
Total time taken = 7 hours
Question : 2
A tap takes 36 hours extra to fill a tank due to a leakage equivalent to half of its inflow. The inflow can fill the tank in how many hours ?
a) 18 hrs
b) 30 hrs
c) 36 hrs
d) 24 hrs
Answer »Answer: (a)
Using Rule 7,
Let the inflow fill the tank in x hours.
$1/x - 1/{2x} = 1/36$
[leakage being half of inflow]
= ${2 - 1}/{2x} = 1/36$
2x = 36
$x = 36/2$ = 18 hours
Question : 3
Two pipes A and B can fill a cistern in 37$1/2$ minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled just in half an hour, if the pipe B is turned off after :
a) 9 minutes
b) 5 minutes
c) 15 minutes
d) 10 minutes
Answer »Answer: (a)
Pipe A fills the tank in $75/2$ minutes.
Part of the tank filled by A in 30 minutes
= $2/75 × 30 = 4/5$
Remaining part
= $1- 4/5 = 1/5$
Now, 1 part is filled by pipe B in 45 minutes
$1/5$ part is filled in
= 45 × $1/5$ = 9 minutes
Hence, the pipe B should be turned off after 9 minutes.
Question : 4
A pipe can fill a tank in 24 hrs. Due to a leakage in the bottom, it is filled in 36 hrs. If the tank is half full, how much time will the leak take to empty the tank?
a) 24 hrs
b) 36 hrs
c) 48 hrs
d) 72 hrs
Answer »Answer: (b)
Using Rule 7,
Part of tank emptied by leak in an hour
= $1/36 - 1/24 = {2 - 3}/72 = {–1}/72$
Time taken in emptying the full tank
= 72 hours
Required time = 36 hours
Question : 5
A cistern is normally filled in 8 hours but takes another 2 hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in :
a) 40 hours
b) 25 hours
c) 16 hours
d) 20 hours
Answer »Answer: (a)
Using Rule 7,
Part emptied by the leak in 1 hour
= $1/8 - 1/10 = {5 - 4}/40 = 1/40$
The leak will empty the cistern in 40 hours.
Question : 6
A pipe can fill a cistern in 9 hours. Due to a leak in its bottom, the cistern fills up in 10 hours. If the cistern is full, in how much time will it be emptied by the leak ?
a) 100 hours
b) 90 hours
c) 70 hours
d) 80 hours
Answer »Answer: (b)
Using Rule 7,
Part of the tank emptied by the leak in 1 hour
= $1/9 - 1/10 = {10 - 9}/90 = 1/90$
Required time = 90 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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