# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-8/8

Exercises: Try Out - Set 8: Real exam simulation to sharpen your skills and build confidence. - Problem 8

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## Exercise 8

### Question

export const metadata = {
  title: "Problem 8",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Three years ago, the ratio of Ali's age to Tika's age was <InlineMath math="4:5" />. If the ratio of their ages three years from now is <InlineMath math="5:6" />, then the difference in their current ages is...


### Choices

- [ ] $$2$$ years
- [ ] $$3$$ years
- [ ] $$4$$ years
- [ ] $$5$$ years
- [x] $$6$$ years

### Answer & Explanation

export const metadata = {
  title: "Solution for Problem 8",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/25/2025",
};

Let <InlineMath math="A" /> be Ali's current age and <InlineMath math="T" /> be Tika's current age. Given that the ratio of Ali's age to Tika's age three years ago was <InlineMath math="4:5" />.

<BlockMath math="\begin{aligned} \frac{A - 3}{T - 3} &= \frac{4}{5} \\ 5(A - 3) &= 4(T - 3) \\ 5A - 15 &= 4T - 12 \\ 5A - 4T &= 3 \quad \dots(1) \end{aligned}" />

Three years from now, the ratio of their ages will be <InlineMath math="5:6" />.

<BlockMath math="\begin{aligned} \frac{A + 3}{T + 3} &= \frac{5}{6} \\ 6(A + 3) &= 5(T + 3) \\ 6A + 18 &= 5T + 15 \\ 6A - 5T &= -3 \quad \dots(2) \end{aligned}" />

From equations <InlineMath math="(1)" /> and <InlineMath math="(2)" />, we perform elimination to find the value of <InlineMath math="A" />. Multiply equation <InlineMath math="(1)" /> by <InlineMath math="5" /> and equation <InlineMath math="(2)" /> by <InlineMath math="4" />.

<BlockMath math="\begin{aligned} 25A - 20T &= 15 \\ 24A - 20T &= -12 \\ \hline A &= 27 \end{aligned}" />

Ali's current age is <InlineMath math="27" /> years. Next, we substitute <InlineMath math="A = 27" /> into equation <InlineMath math="(1)" /> to find <InlineMath math="T" />.

<BlockMath math="\begin{aligned} 5(27) - 4T &= 3 \\ 135 - 4T &= 3 \\ 4T &= 132 \\ T &= 33 \end{aligned}" />

Thus, Tika's current age is <InlineMath math="33" /> years. The difference in their ages is:

<BlockMath math="33 - 27 = 6 \text{ years}" />


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