Pipes and Cistern

Pipes and Cistern

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Question 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
140 gallons
Question 1 Explanation: 
Work done by the waste pipe in 1 minute =1/15-1/20+1/24 = 1/12-11/120 = - 1/40 . [-ve sign means emptying] Volume of 1/40part = 3 gallons. Volume of whole = (3 x 40) gallons = 120 gallons.
Question 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
Question 2 Explanation: 
Suppose pipe A alone takes x hours to fill the tank. Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank. 1/x+2/x+4/x=1/5 ==>7/x=1/5 ==>x = 35 hrs.
Question 3
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 min
B
15 min
C
25 min
D
50 min
Question 3 Explanation: 
Part filled by A in 1 min = 1/20 Part filled by B in 1 min = 1/30 Part filled by (A + B) in 1 min =1/20+1/30 =1/12 . Both pipes can fill the tank in 12 minutes.
Question 4
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.
Question 4 Explanation: 
Let the slower pipe alone fill the tank in x minutes. Then, faster pipe will fill it in x/3 minutes. 1/x+3/x=1/36 ==> 4/x=1/36 x = 144 min.
Question 5
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
Question 5 Explanation: 
Part filled by (A + B) in 1 minute = 1/60+1/40=1/24 . Suppose the tank is filled in x minutes. Then, x/2*(1/24 + 1/40)= 1 x/2*x/15= 1 x = 30 min.
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