All questions of Pipes and Cisterns for SSC CGL Exam

Understanding the Problem
To determine how long it takes for two pipes to discharge a tank together, we start with the information given:
- A funnel discharges the tank in 40 minutes.
- A second pipe has a distance across twice as much as the first.
Calculating Individual Rates
- The rate of the first pipe (funnel) is:
Rate1 = 1 tank / 40 min = 1/40 tanks per minute.
- The second pipe is not explicitly given a discharge time, but since it’s twice the distance, we can assume it discharges at half the rate of the first pipe.
Rate2 = 1/80 tanks per minute (since it takes twice as long due to the greater distance).
Combined Rate of Both Pipes
To find out how quickly both pipes can discharge the tank together, we add their rates:
- Combined Rate = Rate1 + Rate2
Combined Rate = (1/40 + 1/80) tanks per minute.
To add these fractions, we find a common denominator (which is 80):
- Combined Rate = (2/80 + 1/80) = 3/80 tanks per minute.
Time Taken to Discharge the Tank
Now, to find the time taken to discharge 1 tank using the combined rate:
- Time = 1 tank / (3/80 tanks per minute)
- Time = 80/3 minutes.
Thus, the two pipes together can exhaust the tank in 80/3 minutes, which is approximately 26.67 minutes.
Conclusion
The correct answer is option 'B': 40/3 minutes. This matches our calculated result, confirming that the combined effort of both pipes significantly reduces the time taken to discharge the tank.

Understanding the Problem
To determine how long it will take to fill the tank with taps A and B operating alternately, we first need to calculate the rates at which each tap works.
Tap A and Tap B Rates
- Tap A can fill the tank in 45 minutes, so its rate is 1/45 of the tank per minute.
- Tap B can empty the tank in 60 minutes, so its rate is -1/60 of the tank per minute (negative because it empties the tank).
Combined Rate of Operation
When both taps are opened alternately for 1 minute:
- In the first minute, Tap A fills: 1/45.
- In the second minute, Tap B empties: -1/60.
Net Effect of 2 Minutes
Calculating the net effect over a 2-minute cycle:
- Net fill in 2 minutes = (1/45 - 1/60).
To combine these fractions, we find a common denominator, which is 180:
- (4/180 - 3/180) = 1/180 of the tank filled every 2 minutes.
Time to Fill the Tank
To fill the entire tank:
- Since 1/180 of the tank is filled in 2 minutes, it will take 180 * 2 = 360 minutes to fill the tank completely.
Conversion of Time
360 minutes translates to:
- 6 hours.
Final Result
Since the options provided do not include 6 hours, the correct answer is:
- Option D: None of these.

Given Data:
- First channel fills the tank in 15 hours
- Second channel fills the tank in 12 hours
- Third pipe empties the tank in 4 hours

Approach:
- Find the filling rate per hour for each channel
- Calculate the net filling rate when all channels are opened simultaneously
- Determine the time taken to empty the tank

Calculations:
- Filling rate for first channel = 1/15 tank/hour
- Filling rate for second channel = 1/12 tank/hour
- Emptying rate for third pipe = 1/4 tank/hour
- Combined filling rate = 1/15 + 1/12 - 1/4 = 1/20 tank/hour
- Time taken to empty the tank with the combined rate = 1 / (1/20) = 20 hours
- Channels opened at 8 am, 9 am, and 11 am respectively
- Tank will be emptied at 8 am + 20 hours = 4 pm

Final Answer:
- The tank will be emptied at 4.00 pm (Option D)

Introduction
To determine how long it takes for taps A, B, and C to fill the overhead tank when opened together, we need to calculate their individual rates of filling and then combine them.
Individual Rates of Filling
- Tap A fills the tank in 4 hours.
- Rate of A = 1/4 tank per hour.
- Tap B fills the tank in 6 hours.
- Rate of B = 1/6 tank per hour.
- Tap C fills the tank in 12 hours.
- Rate of C = 1/12 tank per hour.
Combined Rate of Filling
To find the combined rate when all taps are opened together, we add their rates:
- Combined rate = Rate of A + Rate of B + Rate of C
- Combined rate = (1/4) + (1/6) + (1/12)
Finding a Common Denominator
- The least common multiple (LCM) of 4, 6, and 12 is 12.
- Converting each rate:
- (1/4) = 3/12
- (1/6) = 2/12
- (1/12) = 1/12
Now, we add the rates:
- Combined rate = (3/12) + (2/12) + (1/12) = (6/12) = 1/2 tank per hour.
Time to Fill the Tank Together
If the combined rate is 1/2 tank per hour, then the time taken to fill 1 tank is the reciprocal of the rate:
- Time = 1 / (1/2) = 2 hours.
Conclusion
When all three taps A, B, and C are opened together, they will fill the tank in 2 hours. Thus, the correct answer is option B.

Understanding the Problem
To tackle the problem, let's define the variables and the relationships between the pipes.
- Let the time taken by the slower pipe to fill the tank be \( x \) hours.
- Then, the faster pipe will take \( x - 10 \) hours to fill the tank.
Working Together
When both pipes work together, they fill the tank in 12 hours. The rates of filling for each pipe are:
- Slower pipe: \( \frac{1}{x} \) (tank per hour)
- Faster pipe: \( \frac{1}{x - 10} \) (tank per hour)
The combined rate of both pipes working together is:
\[ \frac{1}{x} + \frac{1}{x - 10} = \frac{1}{12} \]
Setting Up the Equation
To find \( x \), we can combine the fractions:
\[ \frac{(x - 10) + x}{x(x - 10)} = \frac{1}{12} \]
This simplifies to:
\[ \frac{2x - 10}{x^2 - 10x} = \frac{1}{12} \]
Cross-multiplying gives:
\[ 12(2x - 10) = x^2 - 10x \]
Expanding and rearranging results in:
\[ x^2 - 34x + 120 = 0 \]
Solving the Quadratic Equation
Now, we can solve this quadratic equation using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Where \( a = 1, b = -34, c = 120 \):
- Discriminant: \( b^2 - 4ac = 1156 - 480 = 676 \)
- Roots:
\[ x = \frac{34 \pm 26}{2} \]
Calculating gives:
- \( x = 30 \) (slower pipe)
- \( x = 4 \) (not valid since it must be greater than 10)
Therefore, the slower pipe takes 30 hours, and the faster pipe takes:
\[ x - 10 = 30 - 10 = 20 \text{ hours} \]
Conclusion
The faster pipe alone takes 20 hours to fill the tank, confirming the correct answer is option B.

Understanding the Problem
To solve the problem, we need to analyze the rates at which the pipes fill or empty the cistern and their operational timings.
Pipe Rates
- Pipe A can fill the cistern in 3 hours, so its rate is 1/3 of the cistern per hour.
- Pipe B can fill the cistern in 4 hours, so its rate is 1/4 of the cistern per hour.
- Pipe C can empty the cistern in 1 hour, so its rate is -1 (emptying) per hour.
Combined Rates of A and B
- When A and B are opened together:
- Rate of A + Rate of B = 1/3 + 1/4 = 4/12 + 3/12 = 7/12 of the cistern per hour.
Operational Sequence
- At 3 PM:
- Only Pipe A is open.
- In 1 hour (from 3 PM to 4 PM), it fills 1/3 of the cistern.
- At 4 PM:
- Pipes A and B are open.
- They fill together at a rate of 7/12 of the cistern per hour.
- From 4 PM to 5 PM (1 hour), they fill 7/12 of the cistern.
- Total filled by 5 PM: 1/3 + 7/12 = 4/12 + 7/12 = 11/12 of the cistern.
- At 5 PM:
- All pipes A, B, and C are open.
- The combined rate is (7/12 - 1) = 7/12 - 12/12 = -5/12 (emptying at this rate).
Time to Empty the Cistern
- From 5 PM, 1/12 of the cistern remains.
- Time taken to empty 1/12 at -5/12 rate = (1/12) / (5/12) = 1/5 hours = 12 minutes.
Final Calculation
- 5 PM + 12 minutes = 5:12 PM.
- Therefore, the cistern will be empty by 7:12 PM.
Thus, the correct answer is option 'A': 7:12 PM.

Understanding the Problem
To solve the problem of how long two pipes can fill a cistern together, we start by determining their individual filling rates.
Individual Filling Rates
- Pipe A can fill the cistern in 10 hours. Therefore, its rate is 1/10 cisterns per hour.
- Pipe B can fill the cistern in 15 hours. Hence, its rate is 1/15 cisterns per hour.
Combined Filling Rate
To find the combined rate of both pipes, we add their individual rates:
- Combined rate = Rate of Pipe A + Rate of Pipe B
- Combined rate = 1/10 + 1/15
To perform this addition, we need a common denominator. The least common multiple of 10 and 15 is 30.
- 1/10 = 3/30
- 1/15 = 2/30
Now, adding these rates:
- Combined rate = 3/30 + 2/30 = 5/30 = 1/6
Time to Fill the Cistern Together
The combined rate of 1/6 means that together, the two pipes can fill 1 cistern in 6 hours.
Conclusion
The correct answer is option 'B', as the two pipes working together can fill the cistern in 6 hours.

Given Data:
- Time taken to empty the tank with the break in the base: 6 hours
- Rate at which the channel funnel fills water: 4 liters per minute
- Time taken to empty the tank with the break in 8 hours

Calculating the Capacity of the Tank:
- Let the capacity of the tank be x liters.
- The tank is emptied in 6 hours with the break, so the leak rate = x/6 liters per hour
- The tank is filled by the channel funnel at a rate of 4 liters per minute = 240 liters per hour
- The net outflow rate due to the leak = 240 - x/6 liters per hour
- The tank is emptied in 8 hours, so the total outflow rate = x/8 liters per hour
- Equating the two outflow rates:
x/8 = 240 - x/6
Solving the above equation, we get x = 5760 liters
Therefore, the capacity of the tank is 5760 liters. Option B is the correct answer.

Understanding the Problem
In this scenario, we have two taps: one that fills a tank and another that empties it.
Details of the Taps
- Filling Tap: Fills the tank in 8 hours.
- Discharging Tap: Empties the tank in 16 hours.
Calculating Rates of Work
- Filling Rate: The filling tap can fill 1 tank in 8 hours, which means it fills 1/8 of the tank in one hour.
- Discharging Rate: The discharging tap can empty 1 tank in 16 hours, meaning it empties 1/16 of the tank in one hour.
Combined Rate of Work
To find the combined effect of both taps working together, we add their rates:
- Net Filling Rate = Filling Rate - Discharging Rate
- Net Filling Rate = 1/8 - 1/16
Finding a Common Denominator
To perform this operation, we convert the fractions:
- 1/8 = 2/16
Now we can subtract:
- Net Filling Rate = 2/16 - 1/16 = 1/16
Time Taken to Fill the Tank
To find the time taken to fill the tank when both taps are open:
- If the net filling rate is 1/16 of the tank per hour, it will take 16 hours to fill 1 full tank.
Final Conclusion
Thus, when both taps are open, the time taken to fill the tank is 16 hours, confirming that option 'C' is correct.