Saturday, 27 February 2016

MATHS (SOLVED IN STEPS) PIPES AND CISTERNS - (Page -1)

MATHS (SOLVED IN STEPS)
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:
A. 250 gallons         B. 450 gallons
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
(Continue....)
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