Question

In a mixture of 120 L, the ratio of milk and wateris 2:3. if 30 L mixture is replaced by 18 L of milk and 12 L of water,then new ratio of milk and water is

Answer 1

Quantity of milk = 60 x 2 litres = 40 litres.

3

Quantity of water in it = (60- 40) litres = 20 litres.

New ratio = 1 : 2

Let quantity of water to be added further be x litres.

Then, milk : water = 40 .

20 + x

Now, 40 = 1

20 + x 2

20 + x = 80

x = 60.

Quantity of water to be added = 60 litres.

Answer 2

Given: In a mixture of 120 L, the ratio of milk and water is 2:3. 30 L mixture is replaced by 18 L of milk and 12 L of water.

To find: The new ratio of milk and water.

Solution:

Since the ratio of water to milk is given as 2:3, let the amount of water be 2x and the milk be 3x. So, the amount of the mixture would be (2+3)x which is 5x. Now, the amount of milk and water in the mixture is calculated as follows.

$Milk = \frac{2x}{5x} * 120L$

         $= 48L$

$Water = \frac{3x}{5x} * 120L$

           $= 72 L$

As 30 L of the mixture is removed, the amount of water and milk in the 30 L is calculated as follows.

$Milk = \frac{2x}{5x} * 30L$

         $= 12 L$

$Water = \frac{3x}{5x} * 30L$

           $= 18 L$

So the mixture contained 48 L of milk and then, 12 L of it was replaced by 18 L. Similarly, the mixture contains 72 litres of water and then, 18 L of it was replaced by 12 L. Hence, the final amount of milk and water in the mixture is calculated as follows.

$Milk = 48 - 12 + 18$

         $= 54 L$

$Water = 72 - 18 +12$

           $= 66 L$

The new ratio of milk to water is calculated as,

$\frac{milk}{water} = \frac{54}{66}$

         $= \frac{9}{11}$

         $= 9:11$

Therefore, the new ratio of milk and water is 9:11.