# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-9/12

Exercises: Try Out - Set 9: Real exam simulation to sharpen your skills and build confidence. - Problem 12

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## Exercise 12

### Question

export const metadata = {
  title: "Problem 12",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

A team consists of <InlineMath math="12" /> people who can finish a job in <InlineMath math="15" /> days. If the job needs to be completed faster in <InlineMath math="9" /> days, the percentage increase in workers needed to finish the job is...


### Choices

- [ ] $$25.0\%$$
- [ ] $$37.5\%$$
- [ ] $$50.0\%$$
- [ ] $$62.5\%$$
- [x] $$66.7\%$$

### Answer & Explanation

export const metadata = {
  title: "Solution for Problem 12",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

This problem can be solved using inverse proportion.

Given:

<MathContainer>
  <BlockMath math="12 \text{ people} \rightarrow 15 \text{ days}" />
  <BlockMath math="x \text{ people} \rightarrow 9 \text{ days}" />
</MathContainer>

#### Calculating the Number of Workers Needed

Thus, we can write:

<MathContainer>
  <BlockMath math="\frac{12}{x} = \frac{9}{15}" />
  <BlockMath math="x = \frac{12 \cdot 15}{9}" />
  <BlockMath math="x = 20" />
</MathContainer>

So, the number of workers needed to finish in <InlineMath math="9" /> days is <InlineMath math="20" /> workers.

#### Calculating the Percentage Increase

Thus, the percentage increase in workers is:

<MathContainer>
  <BlockMath math="\frac{20 - 12}{12} \times 100\% = \frac{8}{12} \times 100\% = 66.7\%" />
</MathContainer>


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