# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-10/12

Exercises: Try Out - Set 10: Real exam simulation to sharpen your skills and build confidence. - House Construction Completion

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## Exercise 12

### Question

export const metadata = {
  title: "House Construction Completion",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

To build a house, a contractor needs <InlineMath math="33" /> workers for <InlineMath math="21" /> days. If only <InlineMath math="14" /> workers arrive, how long will they take to complete the job?


### Choices

- [ ] $$48$$ days
- [ ] $$48.5$$ days
- [ ] $$49$$ days
- [x] $$49.5$$ days
- [ ] $$50$$ days

### Answer & Explanation

export const metadata = {
  title: "House Construction Completion Explanation",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

Given:

<MathContainer>
  <BlockMath math="33 \text{ workers} \rightarrow 21 \text{ days}" />
  <BlockMath math="14 \text{ workers} \rightarrow x \text{ days}" />
</MathContainer>

Using inverse proportion:

<MathContainer>
  <BlockMath math="\frac{33}{14} = \frac{x}{21}" />
</MathContainer>

<MathContainer>
  <BlockMath math="14x = 33 \times 21" />
</MathContainer>

<MathContainer>
  <BlockMath math="14x = 693" />
</MathContainer>

<MathContainer>
  <BlockMath math="x = \frac{693}{14}" />
</MathContainer>

<MathContainer>
  <BlockMath math="x = 49.5" />
</MathContainer>

Thus, they can complete the job in <InlineMath math="49.5" /> days.


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