Model 3 Opening both taps and leaks 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 : 1 [SSC CPO S.I.2009]
Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2 hours, C is closed and A and B fill it in 7 hours more. The time taken by C alone to fill the cistern is
a) 17 hours
b) 16 hours
c) 14 hours
d) 15 hours
Answer »Answer: (c)
Part of the cistern filled by pipes A, B and C in 1 hour = $1/6$
Part of the cistern filled by all three pipes in 2 hours = $1/3$
Remaining part =$1– 1/3 = 2/3$
Now, pipe A and B fill $2/3$ part of the cistern in 7 hours
Pipe A and B will fill the cistern in ${7 × 3}/2 = 21/2$ hours
Part of the cistern filled by Aand B in 1 hour = $2/21$
So Part of the cistern filled by C in 1 hour = $1/6 - 2/21$
= ${7 - 4}/42 = 1/14$
Pipe C will fill the cistern in 14 hours.
Question : 2 [SSC CGL Prelim 2002]
A pipe can fill a tank with water in 3 hours. Due to leakage in bottom, it takes 3$1/2$ hours to fill it . In what time the leak will empty the fully filled tank ?
a) 10$1/2$ hours
b) 6$1/2$ hours
c) 12 hours
d) 21 hours
Answer »Answer: (d)
Using Rule 7,
Let the leak empty the full tank in x hours.
$1/3 - 1/x = 2/7$
$1/x = 1/3 - 2/7 = {7 - 6}/21$
$1/x = 1/21 ⇒ x = 21$ hours
Question : 3 [SSC CPO S.I.2006]
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.
Question : 4 [SSC CHSL 2010]
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 : 5 [SSC CGL Tier-I 2015]
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
IMPORTANT quantitative aptitude EXERCISES
Model 3 Opening both taps and leaks Shortcuts »
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