A tank has a leak which would empty the completely filled cistern in 40 hours.…
2025
A tank has a leak which would empty the completely filled cistern in 40 hours. If the tank is full of water and a tap is opened which admits 4 liters of water per minute in the tank, the leak now takes 60 hours to empty the tank. How many liters of water does the tank hold?
Answer: B. 28800 — Given data- Let the total water holding capacity of cistern be x litres A leak which would empty the completely filled cistern in 40 hours ⇒ Rate at which…
- A.
24400
- B.
28800
- C.
23456
- D.
342567
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Correct answer: B
Given data-
Let the total water holding capacity of cistern be x litres
A leak which would empty the completely filled cistern in 40 hours
⇒ Rate at which leak is taken place = x/40 liter/hour → 1
Water is admitted by a pump at the rate of 4 liters/ minute
⇒ Rate at which water is been admitted in cistern = 4 × 60
⇒ Rate at which water is been admitted in cistern = 240 liters/ hour → 2
When both process of leakage and water admission takes place simultaneously
Resultant rate of water leakage =x40−240=x40−240 → 3
It takes 60 hours to empty the tanks with both actions takes place simultaneously
∴ after 60 hours of time water level in cistern will be 0
⇒ Original water level- total water leakage after 60 hours = 0
⇒x−60×(x40−240)=0⇒x−60(x−9600)40=0⇒x−60×(x40−240)=0⇒x−60(x−9600)40=0
⇒ 2x = 3 (x – 9600)
⇒ 2x = 3x – 28800
⇒ x = 28800 liters