Question

Two pipes can separately fill a tank in 20 hrs and 30 hrs respectively. Both the pipes are opened to fill the tank but when the tank is 13 full a leak develops in the tank through which 13 of the water supplied by both the pipes per hour leak out. What is the total time taken to fill the tank?

Answer 1

One pipe fills up 1 / 20th of the tank in one hour while the other fills up 1 / 30th of the tank in one hour. Therefore, together they fill up 1 / 20 + 1 / 30 i.e., (3 + 2) / 60 or 1 / 12th of the tank in one hour. Therefore, together they can fill up the tank in 12 hours but 1 / 3rd of the tank empties because of the leak. Therefore, the pipes need to fill up 1 - 1 / 3 i.e., 4 / 3rd of the tank which will take (4 / 3) / (1 / 12) i.e., 48 / 3 i.e., 16 hours. Ans.

Answer 2

Answer:

The total time taken by both pipes to fill the tank is 16 hours.

 

Step-by-step explanation:

Time taken by Pipe 1 to fill tank = 20 hrs.

Tank filled by pipe 1 in a hour = 1/20

Time taken by Pipe 2 to fill tank = 30 hrs.

Tank filled by pipe 2 in a hour = 1/30

Tank filled by both in a hour = 1/20 + 1/30 = (3 + 2)/60 = 5/60 = 1/12

⇒ Time by by them together to fill the tank = 1/(1/12) = 12 hour

But as we know 1/3rd of tank is empties in a hr.

⇒ Tank that pipes need to fill  = 1 + 1/3 = 4/3

Time taken to fill 4/3 tank by both pipe together = (4/3)/(1/12) = 48/3 = 16

Therefore, The total time taken by both pipes to fill the tank is 16 hours.