1. Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
a) 60 gallons
b) 100 gallons
c) 120 gallons
d) 180 gallons
Explanation: Work done by the waste pipe in 1 minute
$$\eqalign{ & = \frac{1}{{15}} - \left( {\frac{1}{{20}} + \frac{1}{{24}}} \right) \cr & = {\frac{1}{{15}} - \frac{{11}}{{120}}} \cr & = - \frac{1}{{40}}\,\,\,\,\,\left[ { - ve\,{\text{sign}}\,{\text{means}}\,{\text{emptying}}} \right] \cr & {\text{Volume}}\,{\text{of}}\,\frac{1}{{40}}{\text{part}} = 3\,{\text{gallons}} \cr & {\text{Volume}}\,{\text{of}}\,{\text{whole}} \cr & = \left( {3 \times 40} \right){\text{gallons}} \cr & = 120\,{\text{gallons}} \cr} $$
2. A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
a) 20 hours
b) 25 hours
c) 35 hours
d) Cannot be determined
Explanation: Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take $$\frac{x}{2}$$ and $$\frac{x}{4}$$ hours respectively to fill the tank.
$$\eqalign{ & \frac{1}{x} + \frac{2}{x} + \frac{4}{x} = \frac{1}{5} \cr & \frac{7}{x} = \frac{1}{5} \cr & x = 35\,{\text{hours}} \cr} $$
3. Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
a) 1 hours
b) 2 hours
c) 6 hours
d) 8 hours
Explanation: Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours
$$\eqalign{ & \frac{1}{x} + \frac{1}{{ {x + 6} }} = \frac{1}{4} \cr & \frac{{x + 6 + x}}{{x\left( {x + 6} \right)}} = \frac{1}{4} \cr & {x^2} - 2x - 24 = 0 \cr & \left( {x - 6} \right)\left( {x + 4} \right) = 0 \cr & x = 6\,{\kern 1pt} {\kern 1pt} \left[ {{\text{neglecting the negative value of }}x} \right] \cr} $$
4. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
a) 12 minutes
b) 15 minutes
c) 25 minutes
d) 50 minutes
Explanation: Part filled by A in 1 minute = $$\frac{1}{{20}}$$
Part filled by B in 1 minute = $$\frac{1}{{30}}$$
Part filled by (A + B) in 1 minute
$$\eqalign{ & = {\frac{1}{{20}} + \frac{1}{{30}}} = \frac{1}{{12}} \cr} $$
Both pipes can fill the tank in 12 minutes
5.Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
a) 10 min. 20 sec.
b) 11 min. 45 sec.
c) 12 min. 30 sec
d) 14 min. 40 sec.
Explanation:
$$\eqalign{ & {\text{Part}}\,{\text{filled}}\,{\text{in}}\,{\text{4}}\,{\text{minutes}} \cr & = 4\left( {\frac{1}{{15}} + \frac{1}{{20}}} \right) = \frac{7}{{15}} \cr & {\text{Remaining}}\,{\text{part}} = {1 - \frac{7}{{15}}} = \frac{8}{{15}} \cr & {\text{Part}}\,{\text{filled}}\,{\text{by}}\,B\,{\text{in}}\,{\text{1}}\,{\text{minute}} = \frac{1}{{20}} \cr & \frac{1}{{20}}:\frac{8}{{15}}::1:x \cr & x = {\frac{8}{{15}} \times 1 \times 20} \cr & \,\,\,\,\,\, = 10\frac{2}{3}\,\min \cr & \,\,\,\,\,\, = 10\min .\,40\,\sec . \cr & {\text{The}}\,{\text{tank}}\,{\text{will}}\,{\text{be}}\,{\text{full}}\,{\text{in}}\, = {4\min . + 10\min . +\, 40\sec .} \cr & = 14\min .\,40\sec . \cr} $$
6. A tank has a leak which would empty the completely filled tank in 10 hours. If the tank is full of water and a tap is opened which admits 4 litres of water per minute in the tank , the leak takes 15 hours to empty the tank. How many litres of water does the tank hold?
a) 2400 litters
b) 4500 litters
c) 1200 litters
d) 7200 litters
Explanation: Let the total capacity of the tank is 30 units.
The efficiency of Leakage(Pipe A) will be $$\frac{30}{10}$$ = 3
And the efficiency of the leakage (Pipe A) and another Pipe (B) which is filling the tank will be $$\frac{30}{15}$$ = 2
Pipe A is emptying at 3 units/hr and when filling pipe B started then the emptying rate will come down to 2 units/hr.
Filling Pipe B efficiency is 3 - 2 = 1unit/hr
Pipe B will be fill the tank in $$\frac{30}{1}$$ = 30 hrs
Filling rate of Pipe B per minute is 4 litter
Total Capacity of tank will be = (4 × 60) × 30 = 7200 litters
7. A pump can fill a tank with water in 2 hours. Because of a leak, it took $$2\frac{1}{3}$$ hours to to fill the tank. The leak can drain all the water of the tank in?
a) $$4\frac{1}{3}$$ hours
b) 7 hour
c) 8 hour
d) 14 hour
Explanation: Work done by the leak in 1 hour
$$\eqalign{ & {\text{ = }}\left( {\frac{1}{2} - \frac{3}{7}} \right) = \frac{1}{{14}} \cr} $$
Leak will empty the tank in 14 hours.
8. One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in-
a) 81 min
b) 108 min
c) 144 min
d) 192 min
Explanation: Let the slower pipe alone fill the tank in x minutes
Then, Faster pipe alone will fill it in $$\frac{x}{3}$$ minutes
$$\eqalign{ & \frac{1}{x} + \frac{3}{x} = \frac{1}{{36}} \cr & \frac{4}{x} = \frac{1}{{36}} \cr & x = 144 \cr} $$
So slower pipe alone will fill the tank in 144 min.
9. A swimming pool is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the pool in the same time during which the pool is filled by the third pipe alone. The second pipe fills the pool 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?
a) 6 hours
b) 10 hours
c) 15 hours
d) 30 hours
Explanation: Suppose first pipe alone takes x hours to fill the tank.
Then second and third pipes will takes (x - 5) and (x - 9) hours respectively to fill the tank.
$$\eqalign{ & \frac{1}{x} + \frac{1}{{\left( {x - 5} \right)}} = \frac{1}{{\left( {x - 9} \right)}} \cr & \frac{{x - 5 + x}}{{x\left( {x - 5} \right)}} = \frac{1}{{\left( {x - 9} \right)}} \cr & \left( {2x - 5} \right)\left( {x - 9} \right) = x\left( {x - 5} \right) \cr & {x^2} - 18x + 45 = 0 \cr & \left( {x - 15} \right)\left( {x - 3} \right) = 0 \cr & x = 15\left[ {{\text{neglecting }}x\,{\text{ = 3}}} \right] \cr} $$
So, first pipe alone takes 15 hrs to fill the tank.
10. 12 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?
a) 8
b) 15
c) 16
d) 18
Explanation: Capacity of the tank
= (12 × 13.5) litres
= 162 litres
Capacity of each bucket = 9 litres
Number of buckets needed
$$\eqalign{ & {\text{= }}\left( {\frac{{162}}{9}} \right) \cr & = 18 \cr} $$