# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-7/16

Exercises: Try Out - Set 7: 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: "12/26/2025",
};

It is known that the current ratio of Farhat's salary to Abas's salary is <InlineMath math="2 : 3" />. If Farhat and Abas both receive a salary increase of <InlineMath math="40,000" /> rupiah, the ratio of their salaries becomes <InlineMath math="5 : 7" />. What is Abas's current salary?


### Choices

- [ ] $$120,000$$ rupiah
- [ ] $$160,000$$ rupiah
- [ ] $$200,000$$ rupiah
- [x] $$240,000$$ rupiah
- [ ] $$280,000$$ rupiah

### Answer & Explanation

export const metadata = {
  title: "Explanation for Problem 16",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

Let Farhat's salary be <InlineMath math="F" /> and Abas's salary be <InlineMath math="A" />.

The initial ratio of their salaries is given as <InlineMath math="2 : 3" />:

<MathContainer>
  <BlockMath math="F : A = 2 : 3 \Rightarrow F = \frac{2}{3}A" />
</MathContainer>

After both receive a salary increase of <InlineMath math="40,000" /> rupiah, the ratio becomes <InlineMath math="5 : 7" />. To simplify calculations, we will work in thousands (removing the last 3 zeros temporarily), so the increase is <InlineMath math="40" />.

<MathContainer>
  <BlockMath math="(F + 40) : (A + 40) = 5 : 7" />
</MathContainer>

We can write this equation as:
<MathContainer>
  <BlockMath math="\frac{F + 40}{A + 40} = \frac{5}{7}" />
</MathContainer>

Cross-multiply the equation:
<MathContainer>
  <BlockMath math="7(F + 40) = 5(A + 40)" />
</MathContainer>

Substitute <InlineMath math="F = \frac{2}{3}A" /> into the equation:
<MathContainer>
  <BlockMath math="7\left(\frac{2}{3}A + 40\right) = 5(A + 40)" />
  <BlockMath math="\frac{14}{3}A + 280 = 5A + 200" />
</MathContainer>

Group the terms containing <InlineMath math="A" /> on one side and the constants on the other:

<MathContainer>
  <BlockMath math="280 - 200 = 5A - \frac{14}{3}A" />
  <BlockMath math="80 = \frac{15}{3}A - \frac{14}{3}A" />
  <BlockMath math="80 = \frac{1}{3}A" />
</MathContainer>

Multiply both sides by 3 to find the value of <InlineMath math="A" />:
<MathContainer>
  <BlockMath math="A = 80 \times 3" />
  <BlockMath math="A = 240" />
</MathContainer>

Since we used units of thousands, Abas's actual salary is <InlineMath math="240,000" /> rupiah.

Thus, Abas's current salary is <InlineMath math="240,000" /> rupiah.


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