Practice Filling tank by parts or fractions - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) If $3/5$ th of a cistern is filled in 1 minute, the time needed to fill the rest is
(a)
(b)
(c)
(d)
Time taken to fill the $3/5$ of the cistern = 60 seconds
Time taken in filling $2/5$ part
= ${60 × 5}/3 × 2/5$ = 40 seconds
Q-2) 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)
(b)
(c)
(d)
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
= ${4 × 9}/40 = 9/10$
Q-3) 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)
(b)
(c)
(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.
Q-4) 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)
(b)
(c)
(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.
Q-5) 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)
(b)
(c)
(d)
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.
Q-6) $3/4$ 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)
(b)
(c)
(d)
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
Q-7) Pipe A can fill the tank 3 times faster in comparison to pipe B. It takes 36 minutes for pipe A and B to fill the tank together. How much time will pipe B alone take to fill the tank?
(a)
(b)
(c)
(d)
(e)
Let the time taken by pipe B be x minutes
So, the time taken by pipe A = x/3 minutes
Thus, 1/3 + 3/x = 1/36
⇒ 4/x = 1/36
⇒ x = 4×36
⇒ x = 144 minutes
Q-8) 20 buckets can fill a tank when the capacity of each bucket is 12 liters. If the capacity of each bucket is 10 liters, find the number of buckets required to fill the tank.
(a)
(b)
(c)
(d)
Capacity of each bucket = 12 liters
20 buckets can fill the tank. So, capacity of tank = 20 * 12= 240 liters
New capacity of bucket = 10 liters
So, 10 liters can be poured into the tank by one bucket
240 liters will be poured by $1/10$ x 240 = 24 buckets
Q-9) Three pipes A, B and C can fill a tank in 6 hours, 9 hours and 12 hours respectively. B and C are opened for half an hour, then A is also opened. The time taken by the three pipes together to fill the remaining part of the tank is
(a)
(b)
(c)
(d)
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
Q-10) If $1/3$ of a tank holds 80 litres of water, then the quantity of water that $1/2$ tank holds is :
(a)
(b)
(c)
(d)
Let the capacity of the tank be x litres then
$x/3$ = 80 ⇒ x = 240
$x/2 = 240/2$ = 120 litres