Pipes and Cistern
- 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 ?
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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 = 11/20Correct Option: C
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
- Two pipes A and B can fill a tank in 18 and 6 h, respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank ?
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Part filled by A in 1 h = 1/18
Part filled by B in by 1 h = 1/6
Part filled (A + B) in 1 h =1/18 + 1/6 = (1 + 3)/18 = 4/18 = 2/9Correct Option: A
Part filled by A in 1 h = 1/18
Part filled by B in by 1 h = 1/6
Part filled (A + B) in 1 h =1/18 + 1/6 = (1 + 3)/18 = 4/18 = 2/9
Hence, both the pipes together will fill the tank in 9/2 h or 41/2 h
- 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
