 QUESTION

# Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 20kg of fresh grapes?A. 2kgB. 2.4kgC. 2.5kgD. 3kg

Hint: We will find the weight of grapes in 20kg of fresh grapes as $20\times \dfrac{10}{100}=2kg$, then we will find the weight of dried grapes by solving the relation, 80% of x = 2. Here we will find the value of x to get the weight of dried grapes.
Now, we know that in fresh grapes, 90% is the weight of water and the remaining 10% will be the weight of actual grapes. Thus, in 20kg, the actual weight of grapes excluding the water content will be 10% of 20kg. It can be written as, $\dfrac{10}{100}\times 20=2kg$. Thus, in 20kg grapes, we have only 2kg of actual grapes and the rest 18kg is the water content.
Now, we also know that dried grapes contain 20% water, so the remaining 80% will be the actual grapes. Thus, when these 2kg grapes are converted into dried grapes, then we get 80% of x = 2. It can be written as, $\dfrac{80x}{100}=2$.
On cross multiplying, we get $80x=200$.
$x=\dfrac{200}{80}=2.5kg$
Note: Students must be careful while writing the last part of the solution, where they may find 80% of 2kg that is, $\dfrac{80}{100}\times 2=1.6kg$ but actually it is wrong, it is supposed to be 80% of x = 2 that is, $\dfrac{80x}{100}=2$. So, we will get the answer as 2.5kg. So such mistakes must be avoided.