Ashish,
See Nathan's response to your duplicate post of this question. I made a silly mistake. I've removed my answer so it doesn't confuse anyone else.
See Nathan's response to your duplicate post of this question. I made a silly mistake. I've removed my answer so it doesn't confuse anyone else.
Thanks for the feedback.
ASHISH S.
sir in this question why 55 is taken? why n't 56,57,58 were taken?
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09/23/16
Tommy B.
tutor
You have to go in steps so you don't overfill the container. My way was to assume each step of 3 minutes would result in a cistern that was not full. Consider this toy example. Pipe A puts in 1 gallon. Pipe B puts in 1 gallon. Then Pipe C removes 1 gallon. After, A+B-C there is 1 gallon in the tank. But after A and B, there were two gallons in the tank. So, you were spilling water everywhere trying to put in too much.
What I did wrong was I neglected to consider how much water the tank can hold. After 30 minutes with pipe A, the tank would be full. After 20 minutes with pipe B, the tank would be full. After 15 minutes with pipe C, the tank would be empty.
Go in steps. Getting a common denominator helps.
A = (2/60) units/minute
B = (3/60) units/minute
C = (4/60) units/minute
Let's go by minutes.
1 minute, A puts in 2 units.
2 minute, B puts in 3 units.
3 minute, C takes out 4 units.
So, we are left with 1 unit after 3 minutes. We don't want to overfill the tank. How many times can we do the cycle without overfilling the tank? A and B would put in (5/60) units each time they are on. So, let's try 55 cycles (60-5). That would be a tank that is 55/60 full. That is 55 full cycles of 3 minutes per cycle.
55 cycles * 3 minutes/cycle = 165 minutes
The 56th cycle starts with pipe A. We need 1 minute of filling with pipe A. That gives us another 2 units and the tank is (57/60) full.
165 minutes + 1 minute = 166 minutes.
Now run pipe B for 1 minute. This adds 3 more units to the cistern.
166 minute + 1 minute = 167 mintes.
Now the cistern is (60/60) full.
Another way to think about this is by assuming a volume. You might take 60 units as the volume. We can see how much each pipe adds or removes in 1 minute.
A = 60units/30min = 2u/min
B = 60units/20min = 3u/min
C = 60units/15min = 4u/min
We need to get to 60 units. So, we run A, then B, then C for one minute each. That is one cycle.
2u+3u-4u = 1u. (1 unit left in the tank after 3 minutes)
There is one unit of volume in the tank. You can call these gallons if you like.
Run it again,
1u + 2u + 3u - 4u = 2u
Remember that we started with 1u from the first cycle. So, we have 2u in the tank after 6 minutes.
We can run this 60 times and fill the tank! The problem is after 55 full 3 minute cycles, you have 55 units in the tank. If you run the 56th cycle all the way through, then you will have
55u + 2u + 3u - 4u = 56u
The tank isn't full after the cycle but notice that 55u + 2u + 3u = 60u. The tank was full before you opened pipe C.
If you start the 57th cycle, then opening A gives
56u + 2u = 58u
Then open B
58u + 3u = 61u.
Your tank is overflowing. That is why you don't take 56,57,58. This works the same way if you are draining the tank and adding water at the same time. You don'w want to have an empty tank and then add more to it just to empty it! Stop when the tank is full or empty.
I hope this helps you out.
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09/23/16
ASHISH S.
09/23/16