Question

Basic Maths: Time & Work A society’s common tank has two inlet pipes in it, which can fill the tank in 15 and 20 hours respectively. But there is a problem, that there are two leaks in the tank of the same efficiency, one at the bottom of the tank and other at 3/4th height of the tank. Find the time in which the tank will get filled, if the bottom leak can empty the tank in 30 hours. A. 14 hours B. 13 hours C. 18 hours D. 16 hours

Answer 1

Answer:

Let A and B be the two pipes. Then:

20A=1 and

30B=1

Then:

60A=3

60B=2

60A+60B=5

12A+12B=1

A and B can fill the tank, together, in 12 hours.

Then, after 4 hours (1/3 x 12), the leak develops. Then 1/3 of 20A and 30B are leaking, so 2/3 of pipes A and B are filling the tank.

If only 2/3 of the amount being poured through A and B is going into the tank, then the pipes will take 1/ 2/3, or 3/2’s, their usual time. So:

3/2 x 20A=30A

3/2 x 30B=45B

Then:

90A=3

90B=2

90A+90B=5

18A+18B=1

2/3 x 18=12

It will take pipes A and B 12 hours to fill the remaining 2/3rds of the tank.

Add that to the 4 hours it took to fill the first 1/3rd of the tank, it will take 16 hours for the tank to be full

Step-by-step explanation:

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