Question

Fresh fruit contains 68 % water and dry fruit contains 20 % water. How much dry fruit can be obtained from 100 kg of fresh fruits?
(a) 32 kg
(b) 40 kg
(c) 52 kg
(d) 80 kg

Answer 1

Hint: First of all find the fruit content in fresh fruits. Then assume the total quantity of dry fruits as x kg and find the fruit content in dry fruits also. Now equate the fruit content in both cases to find the value of x which is our required answer.

Complete step-by-step answer:
We are given that fresh fruit contains 68 % water and dry fruit contains 20 % water. We have to find the quantity of dry fruit that can be obtained from 100 kg of fresh fruits. Before proceeding with this question, we must know in these types of questions, the water content can change but the fruit content in the particular items will remain the same.
Now let us consider our question. We are given that the total quantity of fresh fruits is 100 kg. So, we are also given that fresh fruits contain 68 % of water. So, we get,
Content of water in fresh fruits = 68 % of 100 kg of fresh fruits
\[\Rightarrow \dfrac{68\times 100kg}{100}=68kg\]
So, we get the content of fruit in total fresh fruit = (Total quantity of fruit – Content of water)
= 100 kg – 68 kg
= 32 kg …..(i)
Now, let us consider the total quantity of the dry fruit to be x kg in 100 kg of fresh fruits. We are given that the dry fruit contains 20 % of water. So, we get,
Content of water in the dry fruit = 20 % of x kg dry fruits.
\[=\dfrac{20\times x}{100}kg\]
So, we get the content of the fruit in total dry fruit = (Total quantity of dry fruit – Content of water)
\[=\left( x-\dfrac{20x}{100} \right)kg\]
\[=\dfrac{\left( 100x-20x \right)}{100}kg\]
\[=\dfrac{80x}{100}kg....\left( ii \right)\]
Now, we know that the fruit content would be the same in both fresh fruits and dry fruit. So, we get,
Fruit content in fresh fruit = Fruit content of dry fruit.
By substituting the respective values from equation (i) and (ii), we get,
\[32kg=\dfrac {80x}{100}\]
By multiplying \[\dfrac{100}{80}\] on both the sides of the above equation, we get,
\[\dfrac{100}{80}\times 32=x\]
\[\Rightarrow x=32\times \dfrac{10}{8}=40kg\]
So, we have obtained 40 kg of dry fruits from 100 kg of fresh fruits.
Hence, option (b) is the right answer.

Note: In these types of questions, students must remember that the content of fruit will remain constant whether dried or fresh. Also, we can directly calculate the content of fruit by calculating 32 % of 100 kg and 80 % of x kg in each case and then equate them. Also, in this question, for better understanding, we can say that fresh fruit is converted into dry fruit and we need to calculate the total quantity of this dry fruit obtained.