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The problem involves distributing a cake among 100 kids, where each successive child receives a percentage of the remaining cake equal to their position in line (e.g., the 1st kid gets 1% of the entire cake, the 2nd kid gets 2% of what's left, and so forth). We need to determine which child receives the largest portion.

To solve this, let's break down the logic:

1. The **1st child** receives 1% of the whole cake, which is \(0.01 \times 100\% = 1\%\).
2. After the 1st child, **99%** of the cake remains.
3. The **2nd child** receives 2% of the remaining 99%, which is \(0.02 \times 99\% = 1.98\%\) of the total cake.
4. After the 2nd child, **97.02%** of the cake remains.
5. The **3rd child** receives 3% of this 97.02%, which is \(0.03 \times 97.02\% = 2.91\%\) of the total cake.

Each subsequent child gets a smaller fraction due to the decreasing percentage of what remains, even though the percentage they receive increases. Since this pattern decreases as we proceed further, the child with the largest share will likely be among the first few.

### Calculation Insight:
The 2nd child typically ends up with the largest portion because while the percentage is slightly less than their position (2%), the remaining cake is still quite substantial (99%).

Thus, the **2nd child** receives the largest portion of the cake.

Would you like to see a more detailed calculation or breakdown? Here are some related questions that might help you explore this further:

1. How do we calculate the exact portion for the 3rd or 4th child?
2. What if the percentage received by each child decreased instead of increased?
3. How would the remaining percentages change after each child's share is taken?
4. What is the total percentage of cake distributed after the first 10 children?
5. How much cake remains after 5 kids have taken their portions?

**Tip**: When dealing with successive percentage-based distributions, calculating each step's remaining fraction is key to understanding the pattern.

On the eve of Annual Function at a school, a huge cake was cut and distributed among 100 kids. First kid gets 1% of total cake, the second kid gets 2% of the remaining cake, the third kid gets 3% of the remaining cake, and so on. Basically, nth kid got n% of the remaining cake. Which nth kid got the largest share of the cake?

Understand how to solve a unique distribution problem where a cake is divided among 100 kids, with each child receiving a successively larger percentage of the remaining cake. Discover which child receives the largest portion using concepts of percentages and successive reductions. Ideal for Grades 10-12.

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