Pipes and Cistern problems
- 1. If two pipes function together, the tank will be filled in 12 h . One pipe fills the tank in 10 h faster than the other. How many hours does the faster pipe take to fill up the tank?
Options- A. 20 h
- B. 60 h
- C. 15 h
- D. 25 h Discuss
Correct Answer: 20 h
Explanation:
Let one pipe takes m h to fill the tank.
Then, the other pipe takes (m - 10) h.
According to the question.
? 1/m + 1/(m - 10) = 1/12
? (m - 10 + m)/{m(m - 10)} = 1/12
? 12m( m - 10 + m ) = ( m - 10 )
? m2 - 34m + 120 = 0
? m2 - 30m - 4m + 120 = 0
? ( m - 30 )( m - 4 ) = 0
? m = 30 or 4
? Faster pipe will take ( 30 - 10 ) h = 20 h to fill the tank.
- 2. A pipe P can fill a tank in 12 min and another pipe R can fill it in 15 min. But, the 3rd pipe M can empty it in 6 min. The 1st two pipes P and R are kept open for double the 2.5 min in beginning and then the 3rd pipe is also opened. In what time is the tank emptied?
Options- A. 30 min
- B. 25 min
- C. 45 min
- D. 35 min Discuss
Correct Answer: 45 min
Explanation:
According to the question,
Double the 2.5 min = 5 min
Now, part filled in 5 min = 5 x ( 1/12 + 1/15 ) = [5 x ( 5 + 4)]/60 = (5 x 9)/60 = 3/4
Part emptied in 1 min when P, R and M, all are opened. = 1/6 - ( 1/12 + 1/5 ) = 1/6 - (5 + 4)/60 = 1/60
One - sixtieth part is emptied in 1 min.
? Three - fourth part will be emptied in 60 x (3/4) = 15 x 3 = 45 min.
- 3. Three pipes A, B and C can fill a tank in 30 min, 20 min and 10 min, respectively. When the tank is empty, all the three pipes are opened. If A, B and C discharge chemical solution P, Q and R respectively, then the part of solution R in the liquid in the tank after 3 min is?
Options- A. 8/11
- B. 5/11
- C. 6/11
- D. 7/11 Discuss
Correct Answer: 6/11
Explanation:
Total quantity of solution P, Q and R from A, B and C receptively, after 3min
= 3/30 + 3/20 + 3/10 = 3 x (2 + 3 + 6)/60 = 11/20
Quantity of solution R in liquid in 3 min = 3/10
? part of solution R = [3/10] / [11/20 ] = (3 x 20)/(10 x 11) = 6/11
- 4. There are 7 pipes attached with a tank out of which some are inlets and some are outlets. Every inlet can fill the tank in 10 h and every outlet can empty the tank in 15 h. When all the pipes are opened simultaneously, the tank is filled up in 2 8/ 11 h. Find the numbers of inlets and outlets.?
Options- A. 5, 2
- B. 6,1
- C. 4,3
- D. 3,4 Discuss
Correct Answer: 5, 2
Explanation:
Let number of outlets be x
? Number of inlets = ( 7 - x )
Time taken to fill the tank when all the pipes are opened = 30/11h
Part of tank filled in 1 h when all the pipes are opened = 11/30 h
According to the question,
(7 - x)/10 - x/15 = 11/30
? {3(7 - x) - 2x}/30 = 11/30
? 21 - 3x - 2x = 11
? 5x = 10
? x = 2
Hence, number of outlets = 2 and number of inlets = 7 - 2 = 5
- 5. Three taps A, B and C fill a tank in 20 min, 15 min and 12 min, respectively. If all the taps are opened simultaneously, how long will they take to fill 40% of the tank?
Options- A. 1 min
- B. 2 min
- C. 3 min
- D. 4 min Discuss
Correct Answer: 2 min
Explanation:
Part of the tank filled in 1 min by A, B and C = 1/20 + 1/15 +1/12
= (3 + 4 + 5)/60 = 12/60 = 1/5
? Time taken by A, B and C to fill the tank = 5 min
? Time taken by A, B and C to fill 40% of the tank = 40% of 5 = (40/100) x 5 = 2 min.
- 6. Capacity of tap B is 80% more than that of A. If both the taps are opened simultaneously, they take 45 h to fill the tank. How long will B take to fill the tank alone?
Options- A. 72 h
- B. 48 h
- C. 66 h
- D. 70 h Discuss
Correct Answer: 70 h
Explanation:
Let time taken by B to fill the tank = T h.
? Time taken by A to fill the tank = T + (T x 80)/100 = 9T/5 h
According to the formula,
Time taken by both the taps to fill the tank = ab /(a + b)
? 45 = (T x 9T/5)/(T + 9T/5)
? 45 x 14T/5 = 9T2/5
? T = 45 x 14/9 = 70 h
- 7. Taps A, B and C are attached with a tank and velocity of water coming through them are 42 L/h, 56 L/h and 48 L/h, respectively. A and B are inlets and C is outlet. If all the taps are opened simultaneously, tank is filled in 16 h. What is the capacity of the tank?
Options- A. 2346 L
- B. 1600 L
- C. 800 L
- D. 960 L Discuss
Correct Answer: 800 L
Explanation:
Quantity of water admitted by tap A in 1 h = 42 L
Quantity of water admitted by tap B in 1h = 56 L
Quantity of water removed by tap C in 1 h = 48 L
So, quantity of water filled in the tank in 1 h = ( 42 + 56 - 48 ) L = 50 L
? Quantity for water filled in 16 h = 16 x 50 = 800 L
Hence, capacity of tank = 800 L
- 8. Two taps A and B can fill a tank in 25 min and 20 min, respectively. But taps are not opened properly so the taps A and B allow 5/6th and 2/3rd part of water, respectively. How long will they take to fill the tank?
Options- A. 12 min
- B. 13 min
- C. 14 min
- D. 15 min Discuss
Correct Answer: 12 min
Explanation:
Part of the tank filled with A and B in
1 min = 1/25 x 5/6 + 1/20 x 2/3 = 1/30 + 1/30
= 2/30 = 1/15
Hence, Time taken to fill the tank = 15 min
- 9. Two taps A and B can fill a tank in 20 min and 30 min, respectively. An outlet pipe C can empty the full tank in 15 min. A, B and C are opened alternatively, each for 1 min. How long will the tank take to be filled?
Options- A. 105 min
- B. 120 min
- C. 167 min
- D. 185 min Discuss
Correct Answer: 167 min
Explanation:
Part of the tank filled by the taps A, B and C in 3 min = 1/20 + 1/30 - 1/15 = (3 + 2 - 4)/60 = 1/60
? Time taken to fill [ 1 - ( 1/20 + 1/30 )] or 55/60th part of the tank = 3 x 55 = 165 min
Remaining part of the tank = 1 - 55/60 = 5/60 = 1/12
Tap A fill 1/0 part in 1 min, then
Remaining part = 1/12 - 1/20 = (5 -3)/60 = 2/60 = 1/30
i.e, 1/30th part is filled by B in 1 min
Hence, required time to fill the whole tank = (165 + 1 +1 ) min = 167 min
- 10. A tank has a leak which would empty it in 8 h. A tap is turned on which admits 3 L a min into the tank and it is now emptied in 12 h. How many litres does the tank hold?
Options- A. 4320 L
- B. 4000 L
- C. 2250 L
- D. 4120 L Discuss
Correct Answer: 4320 L
Explanation:
Work done by the inlet in 1 h = (1/8 - 1/24) = 1/24
Work done by the inlet in 1 min = 1/24 x 1/60 = 1/1440
? Volume of 1/1440 part = 3 L
? Volume of the whole = 3 x 1440 = 4320 L
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