Pipes and Cistern
- A cistern can be filled with water by a pipe in 5 hours and it can be emptied by a second pipe in 4 hours. If both the pipes are opened when the cistern is full, the time in which it will be emptied is :
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According to the question ,
Cistern filled in 1 hour = 1 part 5 Cistern emptied in 1 hour = 1 part 4
When the both pipes are opened, simultaneously ;Cistern emptied in 1 hour = 1 - 1 = 5 - 4 = 1 part 4 5 20 20
∴ The time in which it will be emptied = 20 hours.
Using the given formula :
Here, p = 5, q = 4Required time = pq hrs (p - q)
Correct Option: C
According to the question ,
Cistern filled in 1 hour = 1 part 5 Cistern emptied in 1 hour = 1 part 4
When the both pipes are opened, simultaneously ;Cistern emptied in 1 hour = 1 - 1 = 5 - 4 = 1 part 4 5 20 20
∴ The time in which it will be emptied = 20 hours.
Using the given formula :
Here, p = 5, q = 4Required time = pq hrs (p - q) Required time = 5 × 4 = 20 hrs. 5 - 4
- A tap can empty a tank in one hour. A second tap can empty it in 30 minutes. If both the taps operate simultaneously, how much time is needed to empty the tank?
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We know that , 1 hour = 60 minutes.
Rate of emptying the tank by the two taps are 1 /60 and 1 / 30 of the tank per minute respectively.
When both operate simultaneously ,Rate of emptying the tank = 1 + 1 = 1 + 2 = 3 = 3 of the tank per minute. 60 30 60 60 20
∴ Time taken by the two taps together to empty the tank = 20 minutes
Second method to solve this question :
Here, p = 60, q = 30Required time = pq minutes (p + q)
Correct Option: A
We know that , 1 hour = 60 minutes.
Rate of emptying the tank by the two taps are 1 /60 and 1 / 30 of the tank per minute respectively.
When both operate simultaneously ,Rate of emptying the tank = 1 + 1 = 1 + 2 = 3 = 3 of the tank per minute. 60 30 60 60 20
∴ Time taken by the two taps together to empty the tank = 20 minutes
Second method to solve this question :
Here, p = 60, q = 30Required time = pq minutes (p + q) Required time = 60 × 30 minutes 60 + 30
Required time = 20 minutes.
- Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. If both pipes are opened together, the time taken to fill the tank is :
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As per the given in question , we have
Part of the tank filled by both pipes in one minute = 1 + 1 20 30 Required time = 1 1 + 1 20 30 Required time = 20 × 30 = 12 minutes 50
We can find required answer with the help of given formula :
Here, p = 20, q = 30Required time = pq minutes. p + q
Correct Option: B
As per the given in question , we have
Part of the tank filled by both pipes in one minute = 1 + 1 20 30 Required time = 1 1 + 1 20 30 Required time = 20 × 30 = 12 minutes 50
We can find required answer with the help of given formula :
Here, p = 20, q = 30Required time = pq minutes. p + q Required time = 20 × 30 minutes. 20 + 30
Required time = 12 minutes.