Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits?

### Concept & Logic The core principle in fresh and dry fruit problems is the **Constant Pulp Concept**. Even as water evaporates, the absolute quantity of solid pulp remains completely unchanged. Equating the pulp in fresh fruit to the pulp in dry fruit instantly gives the answer. $$ \text{Pulp in Fresh Fruit} = \text{Pulp in Dry Fruit} $$ ### Step-by-Step Solution * **Given:** * Weight of fresh fruits = $100$ kg * Water in fresh fruit = $68\%$ * Water in dry fruit = $20\%$ * **Calculation:** * Since fresh fruit has $68\%$ water, the solid pulp percentage is $100\% - 68\% = 32\%$. * Amount of pulp in $100$ kg of fresh fruit = $32\%$ of $100 = 32$ kg. * For the dry fruit, the water content is $20\%$, meaning the solid pulp constitutes $100\% - 20\% = 80\%$. * Let the total weight of the dry fruit be $x$. * Since the absolute pulp weight remains constant: $80\%$ of $x = 32$ kg. * $\frac{80}{100} \times x = 32$ * $x = 32 \times \frac{100}{80} = 40$ kg. ### Exam Strategy & Shortcut **Inverse Ratio Method:** Fresh Pulp percentage = $32\%$. Dry Pulp percentage = $80\%$. Ratio of Pulp Percentages = $32 : 80 = 2 : 5$. Because the pulp amount is constant, the ratio of total weights is inversely proportional to their pulp percentages. Ratio of Weights (Fresh : Dry) = $5 : 2$. If $5$ units = $100$ kg (Fresh weight), then $1$ unit = $20$ kg. Therefore, $2$ units = $40$ kg (Dry weight). Solved in seconds! ### Common Pitfall Students often try to calculate the amount of evaporated water and subtract it, which complicates the math and leads to calculation errors. Always focus on the component that does *not* change (the pulp), rather than the one that does (the water). ### Final Answer **Therefore, the correct answer is 40 kg.**