Question

In a mixture of 126 kg of milk and water,milk and water must be added to the mixture to make this ratio 3:2?

Answer 1

I will not follow your solution and will develop my own solution instead. 


In the original mass of 126 kg of the mixture there are 7 (= 5 + 2) equal parts (masses). Hence, the milk contents is  = 5*18 = 90 kg, and water contents is  = 2*18 = 36 kg. OK. Next, the final mixture, having 90 kg of milk, must contain  = 30*2 = 60 kg ow water to provide the ratio  = . Hence, 60 - 36 = 24 kg of water must be added to the original mixture to satisfy the problem requirements.
Answer. 24 kg of water must be added to the original mixture. 

Answer 2

Given:

Ratio of milk and water is 5: 2

Milk and water mixture is of 126 kg

To find:

Water needed to change this ratio to 3: 2

Answer:

Given that milk and water ratio is 5:2

The both mixture is 126 kg

In 126 kg the part of milk is $\frac {5}{7}$and the part of water is $\frac {2}{7}$

So milk quantity is 90 kg and water quantity is 36 kg

Assume x kg is added

Then 90: (36+x) =3:2

$\frac {90}{(36+x)} = \frac {3}{2}$

$3 \times (36+x) =2 \times 90$

$36+x=2 \times \frac {90}{3}$

36+x = 60

x = 60-36

x =24 kg

24 kg of water is added

Thereby, making the ratio to 3:2