Question

A raisin is a dehydrated grape. A natural grape contains 90% of water(by weight), and raisins contain 25% of water(by weight). How much weight of natural grapes (in kg) is required to make 4kgs of raisin?

• A. 30
• B. 35
• C. 40
• D. 45
• E. 50

Hint:

In problems involving dehydration or concentration changes, identify the component that remains constant (the solute or solid part). Set up your equations based on the quantity of this constant component.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a mixture problem focusing on percentages. The key insight is that the amount of solid material (pulp) remains constant when a grape dehydrates into a raisin; only the amount of water changes.
Step 2: Detailed Explanation:
First, let's determine the percentage of pulp in both grapes and raisins.

Natural Grape: Contains 90% water, so it contains \(100% - 90% = 10%\) pulp.
Raisin: Contains 25% water, so it contains \(100% - 25% = 75%\) pulp.
We want to produce 4 kg of raisins. Let's calculate the amount of pulp in these raisins. \[ \text{Weight of pulp in raisins} = 75% \text{ of } 4 \text{ kg} = 0.75 \times 4 = 3 \text{ kg} \] This 3 kg of pulp must have come from the original natural grapes, as the pulp does not change weight. Now, we need to find the total weight of natural grapes that would contain 3 kg of pulp. We know that pulp makes up 10% of the weight of natural grapes.
Let \(W\) be the required weight of natural grapes. \[ 10% \text{ of } W = 3 \text{ kg} \] \[ 0.10 \times W = 3 \] \[ W = \frac{3}{0.10} \] \[ W = 30 \text{ kg} \] Step 3: Final Answer:
To obtain the 3 kg of pulp needed for 4 kg of raisins, 30 kg of natural grapes are required.