You have three Pipes P1, P2, P3 that fill a tank in 5 hours, 10 hours, 15 hours, respectively. You open each pipe, one by one, for exactly two hours and then close it. The pipes start working in the order of P1, P2, and then P3, and half of the tank is now full. In the given scenario, approximately after how long will the tank begin to overflow?
Answers
Answer:
it will take 10 hr 30 minutes to fill the tank
Step-by-step explanation:
5's half is 2.5 hr
10's half is 5 hr
15's half is 7.4 hr
2.5+5+7.4=10.5
5 is 30 minutes because 60/2 is 30
Given : Pipes P1, P2, P3 that fill a tank in 5 hours, 10 hours, 15 hours, respectively
You open each pipe, one by one, for exactly two hours and then close it. The pipes start working in the order of P1, P2, and then P3,
half of the tank is now full
To Find : approximately after how long will the tank begin to overflow
Solution:
pipe 1 in 2 hr = 2/5
pipe 2 in 2 hr = 2/10
pipe 3 in 2 hr = 2/15
Total filled in 6 hrs
= 2/5 + 2/10 + 2/15
= ( 12 + 6 + 4)/30
= 22/30
Remaining = 1 - 22/30 = 8/30 = 4/15
Now pipe 1 take time to fill 4/15
(4/15)/(1/5) = 4/3 hrs
Total Time taken = 6 + 4/3 = 22/3 hrs
Tank over flow in approximately 7.33 hrs
Note :
if Tank was half full before start of pipes
then in 1st 2 hrs by pipe 1
1/2 + 2/5 = 9/10 filled
remaining = 1 - 9/10 = 1/10
1/10 is filled in by pipe 2 in next 1 hr
Then after 3 hrs tank overflow
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