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) 9 minutes
(b) 5 minutes
(c) 15 minutes
(d) 10 minutes
The correct answers to the above question in:
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.
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Read more opening both taps and leaks Based Quantitative Aptitude Questions and Answers
Question : 1
A tank has two pipes. The first pipe can fill it in 4 hours and the second can empty it in 16 hours. If two pipes be opened together at a time, then the tank will be filled in
a) 5$1/3$ hours
b) 6 hours
c) 5$1/2$ hours
d) 10 hours
Answer »Answer: (a)
Using Rule 7,
Part of tank filled by both the pipes in 1 hour
= $1/4 - 1/16 = {4 - 1}/16 = 3/16$
Required time = $16/3 = 5{1}/3$ hours
Question : 2
Two pipes A and B can fill a tank with water in 30 minutes and 45 minutes respectively. The water pipe C can empty the tank in 36 minutes. First A and B are opened. After 12 minutes C is opened. Total time (in minutes) in which the tank will be filled up is :
a) 24
b) 36
c) 30
d) 12
Answer »Answer: (a)
Using Rule 1 and 2,
Part of tank filled by pipes A and B in 1 minute
= $1/30 + 1/45 = {3 + 2}/90 = 1/18$ part
Part of tank filled in 12 minutes
= $12/18 = 2/3$ part
Remaining part
= $1 - 2/3 = 1/3$ part
When pipe C is opened,
Part of tank filled by all three pipes
= $1/30 + 1/45 - 1/36$
= ${6 + 4 - 5}/180 = 5/180 = 1/36$
Time taken in filling $1/3$ part
= $1/3$ × 36 = 12 minutes
Total time = 12 + 12 = 24 miuntes
Question : 3
An empty tank can be filled by pipe A in 4 hours and by pipe B in 6 hours. If the two pipes are opened for 1 hour each alternately with first opening pipe A, then the tank will be filled in
a) 5$1/2$ hours
b) 4$2/3$ hours
c) 1$3/4$ hours
d) 2$3/5$ hours
Answer »Answer: (b)
Part of the tank filled in first 2 hours
= $1/4 + 1/6 = {3 + 2}/12 = 5/12$ Part
Part of the tank filled in first 4 hours
= ${2 × 5}/12$ parts= $5/6$ parts
Remaining part = $1 - 5/6 = 1/6$
Now it is the turn of pipe A
Time taken to fill $1/4$ part = 1 hour
Time taken to fill $1/6$ part
= $1/6 × 4 = 2/3$ hour
Total time = 4 + $2/3 = 4{2}/3$ hours
Question : 4
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 : 5
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 : 6
A tap can fill a cistern in 40 minutes and a second tap can empty the filled cistern in 60 minutes. By mistake without closing the second tap, the first tap was opened. In how many minutes will the empty cistern be filled ?
a) 120
b) 108
c) 72
d) 84
Answer »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.
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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