Model 2 Filling tank by parts or fractions 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) 2$1/2$ hours
(b) 3 hours
(c) 3$1/2$ hours
(d) 2 hours
The correct answers to the above question in:
Answer: (a)
Using Rule 1 and 2,
Part of the tank filled by B and C in half an hour
= $1/2(1/9 + 1/12)$
= $1/2({4 + 3}/36) = 7/72$
= Remaining part
= $1 - 7/72 = {72 - 7}/72 = 65/72$
Part of tank filled by three pipes in an hour
= $1/6 + 1/9 + 1/12$
= ${6 + 4 + 3}/36 = 13/36$
Time to fill remaining part
= $65/72 × 36/13 = 5/2 = 2{1}/2$ hours
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Read more filling tank by parts or fractions Based Quantitative Aptitude Questions and Answers
Question : 1
If $1/3$ of a tank holds 80 litres of water, then the quantity of water that $1/2$ tank holds is :
a) $80/3$ litres
b) 240 litres
c) 100 litres
d) 120 litres
Answer »Answer: (d)
Let the capacity of the tank be x litres then
$x/3$ = 80 ⇒ x = 240
$x/2 = 240/2$ = 120 litres
Question : 2
A tap can fill an empty tank in 12 hours and another tap can empty half the tank in 10 hours. It both the taps are opened simultaneously, how long would it take for the empty tank to be filled to half its capacity ?
a) 15 hours
b) 30 hours
c) 12 hours
d) 20 hours
Answer »Answer: (b)
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
Part of the tank filled in 1 hour
= $1/12 - 1/20 = {5 - 3}/60 = 1/30$
Tank will be filled in 30 hours.
Question : 3
A cistern has two pipes. One can fill it with water in 8 hours and other can empty it in 5 hours. In how many hours will the cistern be emptied if both the pipes are opened together when $3/4$ of the cistern is already full of water ?
a) 6 hours
b) 13$1/3$ hours
c) 3$1/3$ hours
d) 10 hours
Answer »Answer: (d)
Part of cistern emptied in 1 hour
= $1/5 - 1/8 = {8 - 5}/40 = 3/40$
Since, $3/40$ part is emptied in 1 hour.
$3/4$ part is emptied in
$40/3 × 3/4$ = 10 hours.
Question : 4
$3/4$ part of a tank is full of water. When 30 litres of water is taken out, the tank becomes empty. The capacity of the tank is
a) 40 litres
b) 36 litres
c) 38 litres
d) 42 litres
Answer »Answer: (a)
Let the capacity of the tank be x litres.
According to the question,
${3x}/4 = 30$
3x = 30 × 4
$x = {30 × 4}/3$ = 40 litres
Question : 5
Pipes P and Q can fill a tank in 10 and 12 hours respectively and C can empty it in 6 hours. If all the three are opened at 7 a.m., at what time will one-fourth of the tank be filled ?
a) 11 p.m.
b) 10 a.m.
c) 11 a.m.
d) 10 p.m.
Answer »Answer: (d)
Using Rule 2,If x, y, z, ........... all taps are opened together then, the time required to fill/empty the tank will be:$1/x ± 1/y ± 1/z ± ... = 1/T$Where T, is the required timeNote: Positive result shows that the tank is filling and Negative result shows that the tank is getting empty.
Part of tank filled in 1 hour when all three pipes are opened
= $1/10 + 1/12 - 1/6= {6 + 5 - 10}/60 = 1/60$
The tank will be filled in 60 hours.
One fourth of the tank will be filled in 15 hours $[1/4 × 60]$
i.e. the tank will be filled at 10 p.m.
Question : 6
There are two pumps to fill a tank with water. First pump can fill the empty tank in 8 hours, while the second in 10 hours. If both the pumps are opened at the same time and kept open for 4 hours, the part of tank that will be filled up is :
a) $2/5$
b) $9/10$
c) $1/54$
d) $1/10$
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 of the tank filled in an hour by both pumps
= $1/8 + 1/10 = {5 + 4}/40 = 9/40$
Part of the tank filled in 4 hours
= ${4 × 9}/40 = 9/10$
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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