Question

A mixture Contains X litre milk And Y litre Water. If 18Litre of mixture is taken out and replaced with water such that ratio of milk and water becomes 3:1 But If 60 Litre of mixture is taken out and replaced with water then ratio of milk and water becomes 2:3. Find X?​

Answer 1

Given :   A mixture Contains X litre milk And Y litre Water . 18Litre of mixture is taken out and replaced with water ratio of milk and water becomes 3:1 .

To find : Value of X

Solution:

Milk  = X  litre

Water = Y Litre

Total = X + Y  litre

18 litre of mixture is taken out and replaced with Water

=> Milk  = X   -  18X/(X + Y)

=> Water  = Y   - 18Y/(X + Y)   + 18

ratio of milk and water becomes 3:1

=> (X   -  18X/(X + Y) )  / (  Y   - 18Y/(X + Y)   + 18)  = 3/1

=> X   -  18X/(X + Y)  = 3Y - 54Y/(X + Y)   + 54

=>  X² + XY  - 18X  = 3XY + 3Y²  - 54Y  + 54X + 54Y

=> X ² - 3Y²   =  2XY + 72X

if 60 litre of mixture is taken out and replaced with Water

=> Milk  = X   -  60X/(X + Y)

=> Water  = Y   -60Y/(X + Y)   + 60

ratio of milk and water becomes 3:1

=> (X   -  60X/(X + Y) )  / (  Y   - 60Y/(X + Y)   + 60)  = 2/3

=> 3X   -  180X/(X + Y)  = 2Y - 120Y/(X + Y)   + 120

=>  3X² + 3XY  - 180X  = 2XY + 2Y²  - 120Y  + 120X + 120Y

=> 3X ² - 2Y²   =  -XY + 300X

X ² -3Y²   =  2XY + 72X

=> 2X² -  6Y² = 4XY + 144X

3X ² - 2Y²   =  -XY + 300X

=> 9X ² - 6Y²   =  -3XY + 900X

=> 7X² = -7XY + 756X

=> X = Y + 108

=> X + Y = 108

X ² - 3Y²   =  2XY + 72X

=> X²  - 3(108 - X)²  = 2X(108 - X)  + 72X

=> X²  - 3X²  -  3* 108²  +3 *216X  = 216X  - 2X²  + 72X

=>  360X  =  3* 108²

=> X = 97.2

                 

Total        Milk              Water

108 Litre    97.2 Litre   10.8 Litre

108            81                 27

108            43.2             64.8

X = 97.2

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Answer 2

Answer. 97.2L

Step by-step explanation:

here 3:1 ratio means 75%

and 2:3 means 40% concentration

difference in water added is (60-18)L and

percentage is (75-40)%

i.e 42L give 35%

or 5% given by 6L

then 40% by 48L

now look at condition 2:3 or 40% concentration

here 48L was added to get 40%

so total quantity will be 48 + 60 =108L

in 3:1 ratio is 81L and 27L

on removing 18L

81 : 9

i.e initial ratio was 9:1

hence X= (108/10)x9 = 97.2L