Fresh fruit contains 68% water by weight, while dry fruit contains only 20% water. If we start with 100 kg of fresh fruits, how many kilograms of dry fruit can be obtained after removing the excess water, assuming the solid (non-water) content remains unchanged?

Introduction / Context:
This question deals with percentage composition and conservation of the non-water (solid) part of a substance. Fresh fruits and dry fruits differ mainly in their water content. When fresh fruits are dried, water is removed but the solid portion remains the same. The problem asks how much dry fruit can be obtained from 100 kg of fresh fruit, given the water percentages for both types. This type of question is common in percentage and ratio topics in quantitative aptitude.

Given Data / Assumptions:
- Fresh fruit has 68% water and therefore 32% solid content.- Dry fruit has 20% water and therefore 80% solid content.- Initial quantity of fresh fruits = 100 kg.- Water is removed during drying but the solid content is unchanged.- We must find the weight of dry fruit obtained.

Concept / Approach:
The key concept is conservation of solids. When fresh fruit is converted into dry fruit, the amount of solids (non-water portion) stays the same, only the water percentage changes. Thus, we first compute the amount of solid matter in the fresh fruit. Then, we assume this same solid mass is present in the resulting dry fruit, where it represents 80% of the total weight. Using this relationship, we solve for the weight of the dry fruit.

Step-by-Step Solution:
Step 1: Fresh fruits weigh 100 kg.Step 2: Water content in fresh fruits = 68% of 100 kg = 68 kg.Step 3: Solid content in fresh fruits = 100 kg - 68 kg = 32 kg.Step 4: For dry fruit, water content is 20%, so solid content is 80% of its total weight.Step 5: Let the weight of dry fruit be W kg.Step 6: Solid content in dry fruit = 80% of W = (80 / 100) * W = 0.8 * W.Step 7: The solid content must remain the same before and after drying, so:0.8 * W = 32.Step 8: Solve for W: W = 32 / 0.8.Step 9: 32 / 0.8 = 32 * (10 / 8) = 320 / 8 = 40.Therefore, W = 40 kg of dry fruit.

Verification / Alternative check:
Check using percentage reasoning directly.If W = 40 kg, then solid content = 80% of 40 kg = 0.8 * 40 = 32 kg.This matches the original solid content of 32 kg from 100 kg of fresh fruit. Hence, the calculation is consistent and correct.

Why Other Options Are Wrong:
- 20: This would imply solid content of 80% of 20 kg = 16 kg, which is less than the original 32 kg solids.- 30: Gives solids of 0.8 * 30 = 24 kg, which again does not match 32 kg.- 50: Gives solids of 0.8 * 50 = 40 kg, which is more than the original 32 kg and thus impossible without adding extra solids.

Common Pitfalls:
- Trying to directly subtract water percentages (68% - 20%) without considering the conservation of solid mass.- Misinterpreting the percentages as changes in total mass instead of proportions of different states of the same solids.- Forgetting that the fresh fruit and dry fruit masses are different, but the solid mass does not change.- Making arithmetic mistakes when solving 0.8 * W = 32.

Final Answer:
From 100 kg of fresh fruits, we can obtain 40 kg of dry fruit.