Model 2 Filling tank by parts or fractions Practice Questions Answers Test with Solutions & More Shortcuts
pipes & cisterns PRACTICE TEST [3 - EXERCISES]
Model 1 Basic Pipes & Cisterns problems
Model 2 Filling tank by parts or fractions
Model 3 Opening both taps and leaks
Question : 6 [SSC CGL Prelim 2005]
$3/4$ 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 : 7
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) 2$1/2$ hours
b) 3 hours
c) 3$1/2$ hours
d) 2 hours
Answer »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
Question : 8 [SSC CGL Prelim 1999]
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 : 9 [SSC (South Zone) Investigator 2010]
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 : 10
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.
IMPORTANT quantitative aptitude EXERCISES
Model 2 Filling tank by parts or fractions Shortcuts »
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