Solved Problems - Pipes And Cisterns
Solved Problems - Pipes And Cisterns
1. A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in 20 min. How long will the waste pipe take to empty the full cistern?
Answer: 10 minutes
Explanation:
Work done by a waste pipe in 1 minute
= 1 / 20 - ( 1 / 12 + 1 / 15 )
= ( 3 - 5 - 4 ) / 60
= ( -6 / 60 )
= -1 / 10
∴ Waste pipe will empty the full cistern = 10 minutes
2. Two pipes X and Y can fill a tank in 30 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
Answer: 18 hours
Explanation:
Part filled by X in 1 hour = 1 / 30
Part filled by Y in 1 hour = 1 / 45
Part filled by (X+Y) in 1 hour = 1 / 30 + 1 / 45
= ( 3 + 2 ) / 90
= 5 / 90
= 1 / 18
∴ Both the pipes together will fill the tank = 18 hours
3. An electric pump can fill a tank in 2 hours. Because of a leak in the tank, it took 2 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty?
Answer: 10 hours
Explanation:
Work done by the leak in 1 hour = [ 1 / 2 - ( 1 / ( 5 / 2) ) ]
= [ 1 / 2 - 2 / 5 ]
= ( 5 - 4 ) / 10
= 1 / 10
∴ The leak will empty the tank = 10 hours
4. 14 buckets of water fill a tank when the capacity of each bucket is 13 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 10 litres?
Answer: 18 buckets
Explanation:
Capacity of the tank = ( 14 * 13 ) litres
= 182 litres
Capacity of each bucket = 10 litres
So, we can get answer by dividing total capacity of tank by total capacity of bucket
Number of buckets needed = ( 182 / 10)
= 18 buckets
∴ Number of buckets needed = 18 buckets (Approximately)
1. A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in 20 min. How long will the waste pipe take to empty the full cistern?
Answer: 10 minutes
Explanation:
Work done by a waste pipe in 1 minute
= 1 / 20 - ( 1 / 12 + 1 / 15 )
= ( 3 - 5 - 4 ) / 60
= ( -6 / 60 )
= -1 / 10
∴ Waste pipe will empty the full cistern = 10 minutes
2. Two pipes X and Y can fill a tank in 30 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
Answer: 18 hours
Explanation:
Part filled by X in 1 hour = 1 / 30
Part filled by Y in 1 hour = 1 / 45
Part filled by (X+Y) in 1 hour = 1 / 30 + 1 / 45
= ( 3 + 2 ) / 90
= 5 / 90
= 1 / 18
∴ Both the pipes together will fill the tank = 18 hours
3. An electric pump can fill a tank in 2 hours. Because of a leak in the tank, it took 2 hours 30 min to fill the tank. In what time the leak can drain out all the water of the tank and will make tank empty?
Answer: 10 hours
Explanation:
Work done by the leak in 1 hour = [ 1 / 2 - ( 1 / ( 5 / 2) ) ]
= [ 1 / 2 - 2 / 5 ]
= ( 5 - 4 ) / 10
= 1 / 10
∴ The leak will empty the tank = 10 hours
4. 14 buckets of water fill a tank when the capacity of each bucket is 13 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 10 litres?
Answer: 18 buckets
Explanation:
Capacity of the tank = ( 14 * 13 ) litres
= 182 litres
Capacity of each bucket = 10 litres
So, we can get answer by dividing total capacity of tank by total capacity of bucket
Number of buckets needed = ( 182 / 10)
= 18 buckets
∴ Number of buckets needed = 18 buckets (Approximately)
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