Question

from a vessel filled up with pure spirit to the brim, 2 litres of spirit was removed and 2 litres of water were added. after the solution was mixed, 2 litres of the mixture was poured off and again 2 litres of water was added. the solution was stirred again and 2 litres of mixture was removed and 2 litres of water was added. as a result the volume of water is increased by 3 litres than the volume of spirit remaining in it. how many litres of spirit and water was there in the vessel after the above procedure was carried out?​

Answer 1

Given :  A vessel filled up with pure spirit to the brim, 2 litres of spirit was removed and 2 litres of water were added. after the solution was mixed, 2 litres of the mixture was poured off and again 2 litres of water was added. the solution was stirred again and 2 litres of mixture was removed and 2 litres of water was added. as a result the volume of water is increased by 3 litres

To find :  volume of spirit remaining in it. how many litres of spirit and water was there in the vessel after the above procedure was carried out

Solution:

Let say Volume of Spirit   = S  Litre

2 litres of spirit was removed and 2 litres of water were added

=> Spirit = S - 2     & water   = 2  Litre

2 litres of the mixture was poured off and again 2 litres of water was added

Spirit = S - 2  -   2(S-2)/S   =  (S - 2)(1  - 2/S) =  (S- 2)²/S

Water = S -  (S- 2)²/S  or   2  -  2*2/S  + 2   =   4  - 4/S  = 4(S - 1)/S

2 litres of the mixture was poured off and again 2 litres of water was added

Spirt  = (S- 2)²/S    -   2(S- 2)²/S²     = ((S- 2)²/S) ( 1  - 2/S)  = (S- 2)³/S²

Water = S -  (S- 2)³/S²    or  4(S - 1)/S   - 2*4(S - 1)/S²  + 2

S -  (S- 2)³/S²  = 3

=> S³  - (S - 2)³  = 3S²

=>S³   = 3S² + (S - 2)³

=> S³  = 3S²  + S³  - 8   - 6S(S - 2)

=> 0 = 3S² - 8  - 6S²  + 12S

=> 3S² - 12S  + 8  = 0

S = (12 ± √48)/6  =( 12 ± 4√3)/6

=> S = 3.154     or  0.845 (not possible as water increased by 3 litres)

initial Spirit =  3.154 Litre

Final Spirit = 0.154 Litre

Water = 3 Litre

Learn more:

21. A mixture "M1" of Mix Juice, Orange Juice and Pineapple Juice ...

https://brainly.in/question/12864600

A mixture Contains X litre milk And Y litre Water. If 18Litre of mixture ...

https://brainly.in/question/16638491

24 litre of alcohol is mixed with 72 litre of water. x litre of mixture is ...

https://brainly.in/question/13752139