Pipes & Cistern
Important Instructions
Three pipes A, B and C were opened to fill a cistern. Working alone, A, B and C require 12, 15 and 20 minutes respectively.After 4 minutes of working together, A got blocked and after another 1 minute, B also got blocked. C continued to work till the end and the cistern got completely filled. What is the total time taken to fill the cistern ?
Answer: C
Let the capacity of the cistern be LCM(12, 15, 20) = 60 units.
=> Efficiency of pipe A = 60 / 12 = 5 units / minute
=> Efficiency of pipe B = 60 / 15 = 4 units / minute
=> Efficiency of pipe C = 60 / 20 = 3 units / minute
=> Combined efficiency of pipe A, pipe B and pipe C = 12 units / minute
Now, the cistern is filled with the efficiency of 12 units / minute for 4 minutes.
=> Pool filled in 4 minutes = 48 units
=> Pool still empty = 60 – 48 = 12 units
Now, A stops working.
=> Combined efficiency of pipe B and pipe C = 7 units / minute
Now, the cistern is filled with the efficiency of 7 units / minute for 1 minute.
=> Pool filled in 1 minute = 7 units
=> Pool still empty = 12 – 7 = 5 units
Now, B also stops working.
These remaining 5 units are filled by C alone.
=> Time required to fill these 5 units = 5 / 3 = 1 minute 40 seconds
Therefore, total time required to fill the pool = 4 minutes + 1 minutes + 1 minute 40 seconds = 6 minutes 40 seconds
Enter details here
The product of two fractions is 3/4 and their quotient is 6/18. If the denominator of one is 1/3 of the other's numerator, then find the pair of fractions?
Answer: B
Let A = x/y, and B be two fractions
It is given that A×B = 3/4
Therefore x/y × B = 3/4
B = 3y/4x
Therefore, A = x/y and B = 3y/4x
It is given that A/B = (x/y) / (3y/4x) = 6/18
Therefore x/y × 4x/3y = 6 /18
Therefore 4x2/3y2 = 6/18
x2/y2 = 18/(4×18)
Therefore, x2/y2 = 1/4
x/y = 1/2
B = 3y/4x = 3/4 (1/(x/y)) = 3/4 [1/(1/2)] = 6/4
Therefore A = 1/2 and B = 3/2
Enter details here
Due to leakage in a tank, it empties in 6 hours. An inlet pipe fills the water at 4 litres per minute. If the tank is full and inlet is opened the tank empties in 8 hours because of the leakage. What is the capacity of the tank in litres?
Answer: C
Work done by the inlet in 1 hour =
1/6−1/8=1/24
Work done by inlet in 1 min=1/24∗1/60=1/1440
=>Volume of 1/1440 part
= 4 liters
Volume of whole = (1440 * 4) litres = 5760 litres.
Enter details here
3 pipes have diameters 2 cms, 3 cms and 4 cms. The ratio of water flowing through them is equal to ratio of the square of their diameters.The biggest pipe when open alone, can fill the entire pool in just 126 minutes. When all the pipes are opened together, the pool would be filled in how much time?
Answer: A
Enter details here
Two pipes P and Q can fill a tank in 10 hours and 14 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?
Answer: B
Part filled by P in 1 hour = 1/10
Part filled by Q in 1 hour = 1/14
Part filled by (P + Q) in 1 hour = ( 1/10 + 1/14) = (6/35)
Time taken to fill the tank is (35/6) = 5 hours 49 min
Enter details here
A water tank has two pipes to fill water in it. One of the pipes fills water at the rate of 100 litres per hour. The tank is filled by the other pipe in 6 hours and by both pipes together in 4.2 hours. What is the capacity of the tank in litres ?
Answer: D
Let the time taken by the 1st pipe to fill the tank be x hours.
When both the pipes are open, it is given that:
1/x + 1/6 = 1/(4.2) of tank is filled in 1 hour.
1/x + 1/6 = 5/21
21(6 + x) = 30 x
9x = 126
x = 14 hours
Therefore, capacity of the tank = 100 * 14 = 1400 litres.
Enter details here
Two pipes A and B are connected to drain out a water tank. A alone can drain out the tank in 20 hours and B can drain 20 liters per hour. Find the capacity of the water tank given that working together, they require 12 hours to completely drain out the tank.
Answer: A
Let the capacity of the tank be LCM (20, 12) = 60 units
=> Efficiency of A working alone = 60 / 20 = 3 units / hour
=> Efficiency of A and B working together = 60 / 12 = 5 units / hour
Therefore, Efficiency of B working alone = Efficiency of A and B working together – Efficiency of A working alone
=> Efficiency of B working alone = 5 – 3 = 2 units / hour
=> Time required by B alone to drain the tank = 60 / 2 = 30 hours
But we are given that B can drain the tank at the rate of 20 liters per hour.
Therefore, capacity of the water tank = 20 x 30 = 600 liters
Enter details here
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank (in litres) is
Answer: C
Enter details here
Three pipes A, B and C were opened to fill a cistern. Working alone, A, B and C require 12, 15 and 20 minutes respectively. Another pipe D, which is a waste pipe, can empty the filled tank in 30 minutes working alone. What is the total time (in minutes) taken to fill the cistern if all the pipes are simultaneously opened ?
Answer: B
Let the capacity of the cistern be LCM(12, 15, 20, 30) = 60 units.
=> Efficiency of pipe A = 60 / 12 = 5 units / minute
=> Efficiency of pipe B = 60 / 15 = 4 units / minute
=> Efficiency of pipe C = 60 / 20 = 3 units / minute
=> Efficiency of pipe D = 60 / 30 = 2 units / minute
=> Combined efficiency of pipe A, pipe B, pipe C and pipe D = 10 units / minute
Therefore, time required to fill the cistern if all the pipes are opened simultaneously = 60 / 10 = 6 minutes
Enter details here
Topics
- Number System
- H.C.F. & L.C.M.
- Decimal Fractions
- Simplification
- Square Roots & Cube Roots
- Average
- Problems on Numbers
- Problems on Ages
- Surds & Indices
- Operations on Numbers
- Percentage
- Profit & Loss
- Ratio & Proportion
- Partnership
- Chain Rule
- Time & Work
- Pipes & Cistern
- Time & Distance
- Problems on Trains
- Boats & Streams
- Alligation or Mixture
- Simple Interest
- Compound Interest
- Logarithms
- Area
- Volume & Surface Areas
- Mensuration
- Races & Games of Skill
- Calendar
- Clocks
- Stocks & Shares
- Permutations & Combinations
- Probability
- True Discount
- Banker’s Discount
- Heights & Distances
- Odd Man Out & Series
- Algebra
- Divisibility Rules & Remainder Theorem
- Factorials & Power Cycles
- Progressions (A.P., G.P., H.P.)
- Work & Wages
- Set Theory / Venn Diagrams
- Geometry (Lines, Angles, Triangles, Polygons)
- Coordinate Geometry
- Data Interpretation
- Trigonometry
- Statistics (Mean, Median, Mode)
- Arithmetic Operations