Need to find percentage of cream to be added in 6% yogurt

Question

How much cream (at 36% milk fat and 64% water) is necessary to yield 500L of yogurt at 6% milk fat?

Assuming the only source of milk fat is from the cream being added.

Answer 1

To get 500L yogurt of 6% fat, you will need 30L of milk fat. (500*6/100) As your cream has only 36% of milk fat, you need 250/3L of cream. As:

To get 36L of milk fat, you need 100L of cream
To get 1L of milk fat, you need 100/36L of cream
To get 30L of milk fact you need 100*30/36L of cream

Answer = 250/3L of 83.33... L of cream

Hope it helps.

Answer 2

$100$ lit of yogurt contains $6$ lit of fat
$500$ lit of yogurt contains ? lit of fat
? lit=$\large \frac{500 \times 6}{100}=30 $l

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$36$ lit of fat obtained from $100$ lit of cream
$30$ lit of cream obtained from ? lit of cream
? lit=$\large\frac {30 \times 100}{36}=83.33 $ lit