Question

Fresh grapes contain 90% water by weight while dried grapes contain 20% water by weight. What is the weight of dried grapes available from 20 Kg of fresh grapes?
A. 2 kg
B. 2.4 kg
C. 2.5 kg
D. 2.6 kg

Answer 1

Hint: In the process of conversion of fresh grapes to dried grapes only the water content gets changed i.e. water gets evaporated. So, you need to consider the content of fresh grapes excluding water content to be equal to that of dried grapes excluding the water content.

Complete step-by-step answer:
Given,
Water content of fresh grapes = 90% by weight of fresh grapes.
Water content of dried grapes= 20% by weight of dry grapes.
Weight of fresh grapes taken= 20 kg.
Now, to start with the solution, let the weight of the dried grapes which we get from 20 kg of fresh grapes be x kg.
So, the things we get is:
Water content of fresh grapes:
=90% by weight of fresh grapes
$=\dfrac{90}{100}\times \text{(weight of fresh grapes)}$
$=\dfrac{90}{100}\times \text{20kg}$
$=\dfrac{9}{10}\times \text{2kg}$
= 18 kg
$\therefore $ Water content of fresh grapes= 18 kg.
Content of fresh grapes excluding water comes out to be:
(Weight of fresh grapes taken) $-$ (Water content in it)
$=20-18$ kg
$=2$ kg
$\therefore $ Content of fresh grapes excluding water = 2 kg.
Now,
Water content of dried grapes:
= 20% by weight of dried grapes
$=\dfrac{20}{100}\times \text{(weight of dried grapes)}$
$=\left( \dfrac{2}{10}\times x \right)\text{ kg}$
= 0.2x kg
$\therefore $ Water content of dried grapes = 0.2x kg.
Content of dried grapes excluding water comes out to be:
(Weight of dried grapes taken) $-$ (Water content in it)
$=x-0.2x$ kg
$=0.8x$ kg
$\therefore $ Content of dried grapes excluding water $=0.8x$ kg.
Now, as we know, in drying of fresh grapes only the weight of water changes the weight of other contents of grapes remains the same.
$\therefore $ (Content of dried grapes excluding water) = (Content of fresh grapes excluding water)
$\Rightarrow 0.8x=2$
$\Rightarrow x=\dfrac{2}{0.8}$
$\Rightarrow x=2.5$
Therefore, the weight of the dried grapes that we get from 20 kg of fresh grapes $=x=2.5$ kg.
Hence, the answer is option C) 2.5 kg.

Note: Be careful as the percentage of water content is given with respect to the weight in the respective form i.e. 20% in dried grapes refers to 20% of the weight of dried grapes and 90 % of fresh grapes refers to 90% weight of the fresh grapes.