Question

Fresh fruit contains $68\% $ of water and dry fruit contain $20\% $ of water. Then how much dry fruits have in $100$ kilograms fresh fruits?

Answer 1

Hint: The given information is fresh fruit contains $68\% $ of water and dry fruit contains $20\% $of water. The fruit content in both the fresh fruit and dry fruit is the same.
We find how much dry fruits have in $100$ kilograms fresh fruits.
We just use the percentage and division.

Complete step-by-step solution:
The given information is fresh fruit contains $68\% $ of water and dry fruit contains $20\% $ of water.
We find the much dry fruits have in $100$ kilograms fresh fruits.
As fresh fruit contains $68\% $ of water $100$ kilograms fresh fruits, will have $68$ kg of water and hence $100 - 68 = 32$kg of the dried portion.
In dry fruits, we have $20\% $ of water and hence dried portion is $100 - 20 = 80\% $
As such $80$ parts of dried portion makes $100$ parts of dry fruits
Now $1$ part of dried portion makes $\dfrac{{100}}{{80}}$ parts of dry fruits
Also, $32$ kg of dried portion makes $\dfrac{{100}}{{80}} \times 32$ kg of dry fruits
We can write it as,
$ \Rightarrow \dfrac{{100}}{{80}} \times 32$
Multiply$100$by$32$, hence we get
$ \Rightarrow \dfrac{{3200}}{{80}}$
Divide $3200$ by $80$, hence we get
$40$ kg of dry fruits.

Hence, $100$kg of fresh fruits has $40$ kg of dry fruits in them.

Note: This type of sum can be easily done with the help of ratio, no big calculations are required. Also, if you force your brain it can be done orally.
Let’s try another method:
Fresh fruit$ = $water: solid=$68:32 = 17:8;(17 + 8 = 25)$
Dry fruit$ = $ water: solid$ = 20:80 = 5:20;(5 + 20 = 25)$
Now you can see clearly, if you have $100$kg of fresh fruit. It means you have $8 \times 4 = 32$kg the solid part. And in each $25$kg of dry fruit we have $20$kg of the solid part of the fruit.
So $32$kg solid fruit part from the fresh fruit will produce $\left\{ {\left( {25 \div 20} \right) \times 32} \right\} = 40$kg of dry fruits.
So we will get $40$kg of dry fruits from $100$kg of fresh fruits.