# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-5/18

Exercises: Try Out - Set 5: Real exam simulation to sharpen your skills and build confidence. - Question 18

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## Exercise 18

### Question

export const metadata = {
  title: "Question 18",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

An order of <InlineMath math="y" /> dozen clothes can be completed by <InlineMath math="x" /> convection workers in <InlineMath math="20" /> days. If the order must be completed in <InlineMath math="5" /> days, which of the following is the correct relationship between quantity <InlineMath math="P" /> and <InlineMath math="Q" /> based on the information provided?

| <InlineMath math="P" /> | <InlineMath math="Q" /> |
| :---: | :---: |
| Number of workers | <InlineMath math="4x" /> |


### Choices

- [ ] $$P > Q$$
- [ ] $$P < Q$$
- [x] $$P = Q$$
- [ ] $$P + Q = 12x$$
- [ ] The information provided is not sufficient to decide on one of the four choices above

### Answer & Explanation

export const metadata = {
  title: "Answer to Question 18",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

This problem falls into the category of **Inverse Proportion**. If the number of workers increases, the time required to complete the work decreases, and vice versa.

Given:

- <InlineMath math="x" /> workers can complete the order in <InlineMath math="20" /> days.
- The order must be completed in <InlineMath math="5" /> days with <InlineMath math="P" /> workers.

The relationship between the number of workers and the work time can be written as:

<MathContainer>
  <BlockMath math="\text{Number of workers}_1 \times \text{Time}_1 = \text{Number of workers}_2 \times \text{Time}_2" />
</MathContainer>

Substitute the known values:

<MathContainer>
  <BlockMath math="x \cdot 20 = P \cdot 5" />
  <BlockMath math="20x = 5P" />
</MathContainer>

Then the value of <InlineMath math="P" /> is:

<MathContainer>
  <BlockMath math="P = \frac{20x}{5}" />
  <BlockMath math="P = 4x" />
</MathContainer>

It is known that <InlineMath math="Q = 4x" />.

Therefore:

<MathContainer>
  <BlockMath math="P = 4x \quad \text{and} \quad Q = 4x" />
  <BlockMath math="P = Q" />
</MathContainer>

So, the correct relationship is <InlineMath math="P = Q" />.


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