Bank Exam Speed Maths
Page 9: Pipes & Cistern (Shortcut Methods)
1. Basic Concept
Inlet: Fills the tank
Outlet: Empties the tank
Work Concept:
Filling → Positive work
Emptying → Negative work
Filling → Positive work
Emptying → Negative work
2. Efficiency Method
Work rate = 1 / Time
Example:
Pipe A fills tank in 10 hours → 1/10
Pipe B empties in 20 hours → -1/20
Net work = 1/10 - 1/20 = 1/20
Time = 20 hours
Pipe A fills tank in 10 hours → 1/10
Pipe B empties in 20 hours → -1/20
Net work = 1/10 - 1/20 = 1/20
Time = 20 hours
3. LCM Method (Fastest)
Take LCM of given times as total work
Example:
A = 10 hours, B = 20 hours
LCM = 20 units
A fills = 2 units/hour
B empties = -1 unit/hour
Net = 1 unit/hour
Time = 20 hours
A = 10 hours, B = 20 hours
LCM = 20 units
A fills = 2 units/hour
B empties = -1 unit/hour
Net = 1 unit/hour
Time = 20 hours
4. Multiple Pipes Trick
Add all inlet rates and subtract outlet rates
Example:
A = 6 hours → 1/6
B = 8 hours → 1/8
C empties in 12 hours → -1/12
Net work = 1/6 + 1/8 - 1/12 = 1/4
Time = 4 hours
A = 6 hours → 1/6
B = 8 hours → 1/8
C empties in 12 hours → -1/12
Net work = 1/6 + 1/8 - 1/12 = 1/4
Time = 4 hours
5. Alternate Operation
Pipes working alternately:
Calculate work done in cycle (e.g., 2 hours)
Example:
A = 10 hrs, B = 20 hrs
In 2 hours = 1/10 + 1/20 = 3/20
Continue cycle to find total time
A = 10 hrs, B = 20 hrs
In 2 hours = 1/10 + 1/20 = 3/20
Continue cycle to find total time
6. Important Tips
• Treat outlet as negative work
• Use LCM method to avoid fractions
• Always calculate net efficiency
7. Practice Questions
1. A fills in 8 hrs, B empties in 12 hrs → Time?
2. A = 6 hrs, B = 8 hrs, C empties = 24 hrs → Total time?
3. A alone = 10 hrs → Work rate?
4. Two pipes alternate (10 & 15 hrs) → Total time?
5. LCM of 6, 8, 12 → Total work?
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