Pipes and Cistern
- 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?
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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 minCorrect Option: B
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.
- 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?
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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)Correct Option: D
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
- 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?
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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 LCorrect Option: C
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
- 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?
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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 = 1/15Correct Option: A
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
- 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?
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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 minCorrect Option: C
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