Two pipes can fill a tank in 12 and 20 hours respectively. The pipes are open simultaneously and it is found that due to leakage in the bottom, 30 minutes extra are taken for the cistern to be filled up. If the cistern is full, then the time required for the leak to empty it is ____.

Question

Two pipes can fill a tank in 12 and 20 hours respectively. The pipes are open simultaneously and it is found that due to leakage in the bottom, 30 minutes extra are taken for the cistern to be filled up. If the cistern is full, then the time required for the leak to empty it is ____.

Infinity Learn · Accepted Answer

Let the height of cistern as ′H′.The first pipe takes 12 hours to fill the tank.The first pipe fills ‘H12’ height of the cistern in 1 hour.The second pipe takes 20 hours to fill the tank.The second pipe fills ‘H20 ‘ height of the tank in 1 hour.Let us assume that the height of tank filled with both the pipes simultaneously as ‘h’then we get⇒ h= H12+H20Let us assume that both pipes together take ‘t’ time to fill the tank without leakage then we get-⇒t = HH12+H20⇒t = 12×2012+20⇒t = 152hrsHere, we can say that it takes 152 hours to fill the tank by both pipes together.Let us assume that the time taken to fill the tank when there is leakage to empty the tank as 'x'We are given that when both pipes are open it takes 30 minutes extra to fill the tank due to leakageWe know that the conversion of time that is 1hr=60minBy using this conversion we get⇒30min = 1 2 hrNow, by converting the given condition into mathematical equation we get⇒t+12= xNow, by substituting the value of ‘t’ in above equation we get⇒ x =152+12⇒ x=8hrTherefore we can say that it takes 8 hours to fill the tank when there is leakage.So, we can say that both pipes combined with leakage empties 'H8' height of the tank in 1 hour.Let us assume that the leakage takes ‘y’ hours to empty the tank.So, we can say that the leakage empties’ Hy’ height in one hour.Now, we can say that the height filled by both pipes to fill the tank when there is leakage as⇒H12+H20 - Hy=H8⇒1y=112+120-18Now by adding the terms using the LCM we get⇒1y=10+6-15120⇒y=120Therefore, we can say that the leakage takes 120 hours to empty the tank.

Two pipes can fill a tank in 12 and 20 hours respectively. The pipes are open simultaneously and it is found that due to leakage in the bottom, 30 minutes extra are taken for the cistern to be filled up. If the cistern is full, then the time required for the leak to empty it is ____.

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