Question

In container x, the ratio of
Milk and Water is 2: 1, in container y the ratio of water and milk is 2: a. If container x and y are mixed in the ratio of 2:3, to get 100 litres of a mixture having Milk and Water in the ratio 3: 1.
Then a= ?

Answer 1

Answer:

a=2

Step-by-step explanation:

Answer 2

Answer: Value of a is 8.28

Step-by-step explanation:

Volume of mixture = 100 litres

Ratio of x and y in mixture = 2 : 3

Volume of x in mixture = $\frac{2}{2+3} * 100 = 40$ litres

Volume of y in mixture  = 100 - 40 = 60 litres

Ratio of milk and water in x =  2 : 1

Volume of milk in x  = $\frac{2}{3}$ × Volume of x

Volume of milk in mixture through x =  $\frac{2}{3}$ × Volume of x in mixture

Volume of milk in mixture through x = $\frac{2}{3} * 40 = \frac{80}{3}$ litres

Volume of water in mixture through x =  $40 - \frac{80}{3} = \frac{40}{3}$ litres

Ratio of water and milk in y =  2 : a

Ratio of milk and water in y =  a : 2

Volume of milk in y  = $\frac{a}{2+a}$ × Volume of y

Volume of milk in mixture through y =  $\frac{a}{2+a}$ × Volume of y in mixture

Volume of milk in mixture through y = $\frac{a}{2+a} * 60 = \frac{60a}{2+a}$ litres

Volume of water in mixture through y =  $60 - \frac{60a}{2+a} = \frac{120}{a+2}$ litres

Net volume of milk in mixture =  $\frac{80}{3} + \frac{60a}{2+a}$

Net volume of water in mixture = $\frac{40}{3} + \frac{120}{a+2}$

ATQ,

Ratio of milk and water in mixture = 3 : 1

Volume of milk in mixture =  $\frac{3}{3+1} * 100$  litres

Volume of milk in mixture =  75 litres

Volume of water in mixture  =  100 - 75 = 25 litres

Equating the volume of milk in mixture,

$75 = \frac{80}{3} + \frac{60a}{2+a}$

$75 - \frac{80}{3} = \frac{60a}{2+a}$

$\frac{145}{3} = \frac{60a}{a+2} \\145(a+2) = 60a * 3\\145a + 290 = 180a\\290 = 35a\\a = \frac{290}{35}$

a = 8.28

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