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) 4$2/3$
(b) 3$1/4$
(c) 4$1/2$
(d) 3$1/2$
The correct answers to the above question in:
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 tank filled in first two hours
= $1/4 + 1/6 = {3 + 2}/12 = 5/12$
Part of tank filled in first 4 hours
= $10/12 = 5/6$
Remaining part = $1 - 5/6 = 1/6$
This remaining part willl be filled by pipe A.
Time taken by pipe A
= $1/6 × 4 = 2/3$ hour
Total time = 4 + $2/3 = 4{2}/3$ hours
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Read more opening both taps and leaks Based Quantitative Aptitude Questions and Answers
Question : 1
A tank is fitted with two taps. The first tap can fill the tank completely in 45 minutes and the second tap can empty the full tank in one hour. If both the taps are opened alternately for one minute, then in how many hours the empty tank will be filled completely ?
a) 5 hours 53 minutes
b) 4 hours 48 minutes
c) 2 hours 55 minutes
d) 3 hours 40 minutes
Answer »Answer: (a)
Using Rule 7,
Part of the tank filled in one minute
= $1/45 - 1/60 = {4 - 3}/180 = 1/180$
Since, $1/180$ part is filled in 1 minute
$1 - 1/45 = 44/45$ part is filled in
${2 × 180 × 44}/45$ = 352 minutes
i.e. 5 hours 52 minutes
Remaining $1/45$ part will be filled in 1 minute.
Total time taken = 5 hours 53 minutes
Question : 2
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
Question : 3
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 : 4
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. Find the capacity of the tank.
a) 24 litres
b) 10 litres
c) 5760 litres
d) 96 litres
Answer »Answer: (c)
Using Rule 7,
Part of tank filled by inlet pipe in 1 hour
= $1/6 - 1/8 = {4 - 3}/24 = 1/24$
Hence, if there is no leak, the inlet pipe will fill the tank in 24 hours.
Capacity of the tank
= 24 × 60 × 4 = 5760 litres
Question : 5
Pipe A can fill a cistern in 6 hours and pipe B can fill it in 8 hours. Both the pipes are opened simultaneously, but after two hours, pipe A is closed. How many hours will B take to fill the remaining part of the cistern ?
a) 4 hrs
b) 2$2/3$ hrs
c) 2 hrs
d) 3$1/3$ hrs
Answer »Answer: (d)
Using Rule 1,
Part of the cistern filled in 2 hours by pipe A and B
= $2(1/6 + 1/8) =2({4 + 3}/24) = 7/12$
Remaining part =$1 - 7/12 = 5/12$
Time taken by pipe B in filling $5/12$ part
= $5/12 × 8 = 10/3 = 3{1}/3$ hours
Question : 6
A pump can fill a tank with water in 2 hours. Because of a leak in the tank it was taking 2$1/3$ hours to fill the tank. The leak can drain all the water off the tank in :
a) 14 hours
b) 4$1/3$ hours
c) 8 hours
d) 7 hours
Answer »Answer: (a)
Using Rule 7,A tap 'A' can fill a tank in 'x' hours and 'B' can empty the tank in 'y' hours. Then (a) time taken to fill the tankwhen both are opened = $({xy}/{x - y})$ : x > yb) time taken to empty the tankwhen both are opened = $({xy}/{y- x})$ : y > x
Work done in 1 hour by the filling pump = $1/2$
Work done in 1 hour by the leak and the filling pump = $3/7$
Work done by the leak in 1 hour
= $1/2 - 3/7 = {7 - 6}/14 = 1/14$
Hence, the leak can empty the tank in 14 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
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