Mixture Question 1

engg.manik wrote:Q---> A fresh fruit contain 72% water & dry fruit contains 20% water. How many lbs of dry fruit can be obtained from 100lbs of fresh fruits.

It took me a while to determine what this question is asking.
To paraphrase: Fruit consists of water and something we'll call "fruitness." Fresh fruit consists of 72% water and 28% fruitness. Fresh fruit becomes dry fruit once it has lost some water and consists of 20% water and 80% fruitness.

So, let's begin with 100 lbs of fresh fruit. This is comprised of 72 lbs of water and 28 lbs of fruitness.

Let x = the number of lbs of water to be removed such that the fruit becomes dry fruit (20% water).
When we remove x lbs of water, we have 72-x lbs of water remaining
When we remove x lbs of water, we have 100-x lbs of fruit remaining
We want our water to total fruit ratio to equal 20 to 100 (i.e, 20% water)
So, we get the equation: (72-x)/(100-x) = 20/100
To solve:
(72-x)/(100-x) = 1/5 (simplify 20/100)
5(72-x)= 100-x (cross multiply)
etc . . .
x=65
So, we want to remove 65 lbs of water to get our dried fruit.
So, the total weight of the dried fruit will be 35lb (100 lbs - 65 lbs = 35 lbs)

Note: we could have also set up our equation to be:
28/(100-x) = 80/100, where we try to get the fruitness percentage to be 80%. Same outcome.

Another approach is to recognize that dried fruit is 20% water and 80% fruitness.
So, in dried fruit, the ratio of water to fruitness is 20/100 or 1/4
We know that 100 lbs of fresh fruit will contain 28lb of fruitness.
If we let X = the lbs of water that go with the fruitness to create dried fruit, we get the equivalent ratios: x/28 = 1/4
We can easily see that x=7 (7 lbs of water).
So, the total weight of the dried fruit is 28+7=35lbd