Question

There are three types of milk Parag, Amul and nestle.
The ratio of fat to non-fat content in milk is 2:3:, 3:
4, 4: 5 respectively. If all the three types of milk is
mixed in equal quantity, the ratio of fat and non-fat
contents in the mixture will be
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Answer 1

Answer:  The required ratio of fat and non-fat contents in the mixture is 401 : 544.

Step-by-step explanation:  Given that there are three types of milk Parag, Amul and nestle.  The ratio of fat to non-fat content in milk is 2:3:, 3:  4, 4: 5 respectively. All the three types of milk is  mixed in equal quantity.

We are to find the ratio of fat and non-fat  contents in the mixture.

The fat content in Parag, Amul and Nestle milk are

$F_p=\dfrac{2}{2+3}=\dfrac{2}{5},\\\\\\F_a=\dfrac{3}{3+4}=\dfrac{3}{7},\\\\\\F_n=\dfrac{4}{4+5}=\dfrac{4}{9}.$

The non-fat content in Parag, Amul and Nestle milk are

$NF_p=\dfrac{3}{2+3}=\dfrac{3}{5},\\\\\\NF_a=\dfrac{4}{3+4}=\dfrac{4}{7},\\\\\\NF_n=\dfrac{5}{4+5}=\dfrac{5}{9}.$

So, the total fat content and non-fat content in the mixture are given by

$F=F_p+F_a+F_n=\dfrac{2}{5}+\dfrac{3}{7}+\dfrac{4}{9}=\dfrac{401}{315},\\\\\\NF=NF_p+NF_a+NF_n=\dfrac{3}{5}+\dfrac{4}{7}+\dfrac{5}{9}=\dfrac{544}{315}.$

Therefore, the ratio of  fat and non-fat  contents in the mixture is

$F:NF=\dfrac{401}{315}:\dfrac{544}{315}=\dfrac{401}{315}\times\dfrac{315}{544}=\dfrac{401}{544}=401:544.$

Thus, the required ratio of fat and non-fat contents in the mixture is 401 : 544.