# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-6/16

Exercises: Try Out - Set 6: Real exam simulation to sharpen your skills and build confidence. - Problem 16

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## Exercise 16

### Question

export const metadata = {
  title: "Problem 16",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

To complete the construction of a building, <InlineMath math="15" /> people are needed to work for <InlineMath math="35" /> days. However, the building owner wants the building to be finished in <InlineMath math="3" /> weeks. To finish exactly as desired by the building owner, ... additional workers are needed.


### Choices

- [ ] $$30$$
- [ ] $$25$$
- [ ] $$20$$
- [ ] $$15$$
- [x] $$10$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Problem 16",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

This problem involves inverse proportion. If the number of workers increases, the time required decreases, and vice versa.

Given:
*   <InlineMath math="15" /> people can complete the work in <InlineMath math="35" /> days.
*   The work is desired to be completed in <InlineMath math="3" /> weeks <InlineMath math="= 3 \times 7 = 21" /> days.

Let <InlineMath math="P" /> be the total number of workers needed to complete the work in <InlineMath math="21" /> days.

<MathContainer>
  <BlockMath math="\text{Workers}_1 \times \text{Time}_1 = \text{Workers}_2 \times \text{Time}_2" />
  <BlockMath math="15 \times 35 = P \times 21" />
  <BlockMath math="525 = 21P" />
  <BlockMath math="P = \frac{525}{21}" />
  <BlockMath math="P = 25" />
</MathContainer>

So, a total of <InlineMath math="25" /> workers are needed.

The question asks for the **additional** workers.
The initial number of workers is <InlineMath math="15" />.

<MathContainer>
  <BlockMath math="\text{Additional} = \text{Total workers} - \text{Initial workers}" />
  <BlockMath math="\text{Additional} = 25 - 15 = 10 \text{ people}" />
</MathContainer>

Thus, <InlineMath math="10" /> additional workers are needed.


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