Fresh vs dry grapes — Dry grapes contain 25% water and fresh grapes contain 80% water. Akram Miya has 20 kg of dry grapes. He adds water (free) so that the mixture now matches the fresh-grape water proportion (80%), and then sells the entire mixture at the same cost price per kg as dry grapes. What is his total profit percentage?

Introduction / Context: This is a water-content (concentration) and profit question. The key is that the solid grape matter is conserved; adding water increases weight without adding cost. Selling at the dry-grape cost price per kg on the heavier hydrated lot creates profit due purely to the extra water weight.

Given Data / Assumptions:

• Dry grapes: 25% water ⇒ 75% solids.
• Fresh-equivalent target: 80% water ⇒ 20% solids.
• Initial mass of dry grapes = 20 kg (cost incurred on these 20 kg only).
• Added water is free; selling rate per kg remains the dry-grape cost price.

Concept / Approach: Solids are constant during hydration. Let S be solids (kg). In the dry lot, S = 0.75 * 20. After adding water, the final mix has S as 20% of total weight W_final. Solve W_final from S = 0.20 * W_final, then compare revenue vs cost at the same per-kg rate.

Step-by-Step Solution:

Verification / Alternative check: If cost rate is r per kg (for dry), cost = 20r. Revenue = 75r. Profit = 55r ⇒ Profit% = 55r / 20r * 100 = 275%. The value is independent of r.

Why Other Options Are Wrong: 200%, 125%, 160%, and 80% come from incorrect solids calculations or from assuming the final water is 80% of 20 kg instead of solving via conserved solids.

Common Pitfalls: Treating “80% water” as “add 60% water” on the initial mass. Always conserve solids to find the correct final weight when water is added.

Final Answer: 275%