Fresh grapes contain 60% water by weight, while dry grapes contain 40% water by weight. If you start with 60 kg of fresh grapes, how many kilograms of dry grapes will you obtain after drying (assuming only water is removed)?

Introduction / Context:
This is a classic percentage and mixture style problem that uses the concept of constant solids. When fresh grapes are dried, water is removed but the solid portion remains the same. By tracking the solid part before and after drying, we can determine the final weight of the dry grapes. Questions of this type are frequently asked to test logical reasoning with percentages and composition.

Given Data / Assumptions:

Weight of fresh grapes = 60 kg.

Fresh grapes contain 60% water and therefore 40% solids.

Dry grapes contain 40% water and therefore 60% solids.

Only water is removed during drying and the amount of solid matter remains constant.

Concept / Approach:
The key idea is that solid content does not change during drying. First, calculate the amount of solid substance in the fresh grapes. Next, assume that the same amount of solid substance is present in the dry grapes, but it now constitutes 60% of the total weight of the dry grapes. Using this relationship, set up an equation for the unknown final weight and solve it.

Step-by-Step Solution:
Step 1: Fresh grapes are 60% water and 40% solids.Step 2: Solid mass in fresh grapes = 40% of 60 kg = (40 / 100) * 60 = 24 kg.Step 3: In dry grapes, water is 40%, so solids are 60% of the final weight.Step 4: Let the final weight of dry grapes be W kg.Step 5: Since solids remain the same, 60% of W equals 24 kg.That is, (60 / 100) * W = 24.Step 6: Solve for W: W = 24 * 100 / 60 = 24 * (5 / 3) = 40 kg.

Verification / Alternative check:
Check the composition of dry grapes at the final weight. If the final weight is 40 kg and solids are 60%, then solids = 0.60 * 40 = 24 kg, and water = 16 kg. This matches the solid mass we computed from the fresh grapes, so the mass balance is correct.

Why Other Options Are Wrong:
25 kg and 30 kg give too little solid mass if you apply the 60% solids condition, which contradicts the original 24 kg of solids.
35 kg also fails to deliver exactly 24 kg solids when multiplied by 60%, so it cannot be correct.
32 kg is another distractor that does not satisfy the equality of solid mass before and after drying.

Common Pitfalls:
A common mistake is to think that water content alone changes linearly and to subtract percentages incorrectly. Another frequent error is to treat the percentage values as if they apply to the same total weight, rather than recognizing that fresh and dry grapes have different total weights. Always focus on the invariant quantity, which is the solid part, and then express that as a percentage of the new total weight to find the final answer.

Final Answer:
From 60 kg of fresh grapes, you will obtain 40 kg of dry grapes.