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Pipes and cisterns-Hard test 1
A tank has a leak which would empty the completely filled tank in 10 h. If the tank is full of water and a tap is opened which admits 4 L of water per minute in the tank, the leak takes 15h to empty the tank. How many liters of water does the tank hold?
A water tank has three taps A, B and C. A fills four buckets in 24 minutes, B fills 8 buckets in 1 hour and C fills 2 buckets in 20 minutes. If all the taps are opened together, a full tank is emptied in 2 hours. If a bucket can hold 5 liters of water, what is the capacity of the tank?
Answer: Option A
Tap A fills 4 buckets in 24 minutes ⇒
Tap B fills 8 buckets in 1 hour ⇒
Tap C fills 2 bucket in 20 minutes ⇒
In 2 hours,
Number of buckets filled by tap A ⇒
Number of buckets filled by tap B ⇒
Number of buckets filled by tap C ⇒
Total number of buckets filled ⇒ (20 + 16 + 12) = 48 buckets
Total capacity of the tank = Total number of buckets filled X Capacity of each bucket
Two pipes A and B can fill a tank in 24 minutes and 32 minutes respectively. If both the pipes are opened at the same time, after how long should pipe B be closed such that the tank is filled in 18 min?
Answer: Option B
According to the formula, If Two pipes A and B can fill the tank in x and y min respectively. If both pipes are opened together, then the time after which pipe B should be closed so that the tank is full in t min is min.
Hence, the tank will be filled in 8 min both the pipes are opened simultaneously.
In what time a cistern be filled by three pipes whose diameters are 1cm, , 2cm running together, when the largest alone will fill the tank in 61 min. The amount of water flowing in by each pipe being proportional to the square of its diameter?
Answer: Option D
As per the question,
In 1 minute,
Pipe with 2 cm diameter fillsth of the cistern
Pipe with 1 cm diameter fillsth of the cistern
Pipe with cm diameter fillsth of the cistern
∴ In 1 min all the pipes to gether can fill
Hence in 36 Minutes the complete tank will be filled.
Two pipes P and Q will fill a reserviour in 24 hours and 32 hours respectively. if both pipes are opened together, find when the first pipe must be turned off so that the reserviour may be just filled in 16 hours.
Answer: Option C
According to the formula, If Two pipes A and B can fill the tank in x and y min respectively. If both pipes are opened together, then the time after which pipe B should be closed so that the tank is full in t min is hours.
Hence, the tank will be filled in 12 hours both the pipes are opened simultaneously.