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PIPES AND CISTERNS - (Page -1)

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PIPES AND CISTERNS - (Page -1)

1. Two pipes can fill a tank in 25 and 30 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:

C. 120 gallons D. 150
gallons

**Answer: Option B**

**Explanation:**

Part filled
by first pipe in 1 minute= 1/25

Part filled
by second pipe in 1 minute= 1/30

Let the
waste pipe can empty the full tank in x minutes Then, part emptied by waste
pipe in 1 minute= 1/x

All the
three pipes can fill the tank in 15 minutes i.e., part filled by all the three
pipes in 1 minute= 1/15

==>
1/25+1/30-1/x=1/15

==>
1/x=1/25+1/30"1/15 = (6+5-10)/150=1/150

==> x=150

i.e, the
waste pipe can empty the full tank in 150 minutes

Given that
waste pipe can empty 3 gallons per minute ie, in 150 minutes, it can empty 150
x 3 = 450 gallons Hence, the volume of the tank = 450 gallons

2. A tank is filled in 10
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. 70 hours B.
30 hours

C. 35 hours D.
50 hours

**Answer: Option A**

**Explanation:**

Let the pipe
A can fill the tank in x hours

Then pipe B
can fill the tank in x/2 hours and pipe C can
fill the tank in x/4 hours

Part filled
by pipe A in 1 hour = 1/x

Part filled
by pipe B in 1 hour = 2/x

Part filled
by pipe C in 1 hour = 4/x

Part filled
by pipe A, pipe B and pipe C in 1 hour = 1/x+2/x+4/x=7/x

i.e., pipe
A, pipe B and pipe C can fill the tank in x/7 hours

Given that
pipe A, pipe B and pipe C can fill the tank in 10 hours

=>x/7=10

==>x=10x7=70
hours

3. One pipe can fill a tank
four 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. 180 min B.
144 min

C. 126 min D.
114 min

**Answer: Option A**

**Explanation:**

Let the
slower pipe alone can fill the tank in x minutes Then the faster pipe can fill
the tank in x/4 minutes

Part filled
by the slower pipe in 1 minute = 1/x

Part filled
by the faster pipe in 1 minute = 4/x

Part filled
by both the pipes in 1 minute = 1/x+4/x

It is given
that both the pipes together can fill the tank in 36 minuts

Part filled
by both the pipes in 1 minute = 1/36

1/x+4/x=1/36

5/x=1/36

x=5x36=180

ie.,the
slower pipe alone fill the tank in 180 minutes

4. A tap can fill a tank in 4 hours. After half the tank is filled,
three more similar taps are opened. What is the total time taken to fill the
tank completely?

A. 3 hr B.
1 hr 30 min

C. 2 hr 30 min D. 2
hr

**Answer: Option C**

**Explanation:**

A tap can
fill a tank in 4 hours

= > The
tap can fill half the tank in 2 hours

Remaining
part = 1/2

After half
the tank is filled, three more similar taps are opened.

Hence, total
number of taps becomes 4.

Part filled
by one tap in 1 hour = ¼

Part filled by four taps in 1 hour = 4x1/4=1

i.e., 4 taps can fill remaining half in 30 minutes Total time
taken = 2 hour + 30 minute = 2 hour 30 minutes

5. A tap can fill a tank in 4 hours. After half the tank is filled, two
more similar taps are opened. What is the total time taken to fill the tank
completely?

A. 1 hr 20 min B. 4
hr

C. 3 hr D.
2 hr 40 min

**Answer: Option D**

**Explanation:**

A tap can
fill a tank in 4 hours

=> The
tap can fill half the tank in 2 hours

Remaining
part = 1/2

After half
the tank is filled, two more similar taps are opened.

Hence, total
number of pipes becomes 3.

Part filled
by one tap in 1 hour = ¼

Part filled
by three taps in 1 hour = 3x1/4=3/4

Time taken
to fill12the tank by 3 pipes = (1/2) + (3/4) =4/6

==2/3 hour =
40 minutes

Total time
taken = 2 hour + 40 minute = 2 hour 40 minutes

6. Three pipes A, B and C can
fill a tank in 6 hours. After working at
it together for 2 hours, C is closed and A and B can fill the remaining part in
7 hours. The number of hours taken by C alone to fill the tank is:

A. 10 B.
12

C. 14 D.
16

**Answer : Option C**

**Explanation :**

A, B and C
can fill a tank in 6 hours.

==>Part
filled by pipes A,B and C in 1 hr = 1/6

All these
pipes are open for only 2 hours and then C is closed.

Part filled
by pipes A,B and C in these 2 hours = 2/6=1/3

Remaining
part = 1-(1/3)
=2/3

This
remaining part of 2/3 is filled by pipes A and B in 7 hours

===>Part
filled by pipes A and B in 1 hr ={(2/3) + 7} =2/21

Part filled by pipe C in 1 hr = (1/6-2/21)=(7-4)/42=3/42=1/14
i.e., C alone can fill the tank in 14 hours

7. A large tanker can be
filled by two pipes A and B in 60 minutes
and 40 minutes respectively. How many minutes will it take to fill the tanker
from empty state if B is used for half the time and A and B fill it together
for the other half?

A. 15 min B.
20 min

C. 27.5 min D.
30 min

**Answer : Option D**

**Explanation :**

Part filled
by pipe A in 1 minute = 1/60

Part filled
by pipe B in 1 minute = 1/40

Part filled
by both pipes A and pipe B in 1 minute

=
1/60+1/40=(2+3)/120=5/120=1/24

Suppose the
tank is filled in x minutes

Then, To
fill the tanker from empty state, B is used for x/2 minutes and

A and B is
used for the rest x/2 minutes x/2x1/40+x/2x1/24=1

==>x/2[1/40+1/24]=1

==>x/2x8/120=1

==>x/2x1/15=1

x=15x2=30
minutes

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