Question

Fresh grapes contain 80 percent water, while dry grapes contain 10 percent water. If the weight of dry grapes is 250 kg, what was its total weight, when it was fresh?
A. 1000 kg
B. 1125 kg
C. 1225 kg
D. 1100 kg

Answer 1

Hint: The water content in fresh grapes and dry grapes changes but weight of the pulp remains the same. In dry grapes, 10 percent is water and remaining 90 percent is pulp. In fresh grapes, 80 percent is water and remaining 20 percent is pulp. This means 90 percent pulp of dry grapes is equal to 20 percent pulp of fresh grapes. So find the weight of pulp in dry grapes and equate it to 20 percent weight of fresh grapes to find the whole weight of fresh grapes.

Complete step-by-step answer:
We are given that fresh grapes contain 80 percent water, while dry grapes contain 10 percent water.
We have to find the weight of fresh grapes when the weight of its dry grapes is 250 kg.
Let the total weight of fresh grapes be x.
In dry grapes, 10 percent is water and $ 100 - 10 = 90 $ percent is pulp.
In fresh grapes, 80 percent is water and $ 100 - 80 = 20 $ percent is pulp.
Total weight of dry grapes is 250 kg.
90 percent pulp weight of dry grapes is
 $ \Rightarrow \dfrac{{90}}{{100}} \times 250 = 225 $ kg.
This 90 percent weight of dry grapes is equal to the 20 percent weight of fresh grapes (because, the water dries off from the fresh grapes but the pulp remains the same).
Therefore,
 $ \dfrac{{20}}{{100}} \times x = 225 $
 $ \Rightarrow \dfrac{{20}}{{100}} \times x = 225 \to x = \dfrac{{22500}}{{20}} = 1125 $ kg.
Therefore, the weight of fresh grapes is 1125 kg and its weight when dried is 250 kg.
Hence, the correct option is Option B
So, the correct answer is “Option B”.

Note: The amount of pulp remains the same in both fresh grapes and dry grapes, because pulp is a solid and it cannot be evaporated whereas water is a liquid and water evaporates at its boiling point. Percentage is the amount in 100. Instead of using the word “percent”, we can also use the symbol “%” to indicate percentages.