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. 2kg B. 2.4kg C. 2.5kg D. 3kg
ANSWER
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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.
Complete step by step answer: It is given in the question that fresh grapes contain 90% water and dried grapes contain 20% water. Also, we have been given that the total weight of fresh grapes is 20kg. Now, we have to find the weight of dried grapes when this 20kg fresh grape is dried. 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 $80x=200$. $x=\dfrac{200}{80}=2.5kg$ Thus, the total weight of dried grapes is 2.5kg. Hence, option (C) is the correct answer.
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.